Optimal. Leaf size=648 \[ \frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {11275 \sqrt {\frac {1}{2} \left (7+2 \sqrt {14}\right )} \left (9756589235+2148932869 \sqrt {14}\right ) \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}-2 \sqrt {3-2 x}}{\sqrt {-7+2 \sqrt {14}}}\right )}{318603459702399434752}-\frac {11275 \sqrt {\frac {1}{2} \left (7+2 \sqrt {14}\right )} \left (9756589235+2148932869 \sqrt {14}\right ) \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}+2 \sqrt {3-2 x}}{\sqrt {-7+2 \sqrt {14}}}\right )}{318603459702399434752}+\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \sqrt {\frac {1}{2} \left (-7+2 \sqrt {14}\right )} \log \left (3+\sqrt {14}-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{637206919404798869504}-\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \sqrt {\frac {1}{2} \left (-7+2 \sqrt {14}\right )} \log \left (3+\sqrt {14}+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{637206919404798869504} \]
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Rubi [A]
time = 0.71, antiderivative size = 648, normalized size of antiderivative = 1.00, number of steps
used = 29, number of rules used = 9, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.450, Rules used = {754, 836, 842,
840, 1183, 648, 632, 210, 642} \begin {gather*} \frac {11275 \sqrt {\frac {1}{2} \left (7+2 \sqrt {14}\right )} \left (9756589235+2148932869 \sqrt {14}\right ) \text {ArcTan}\left (\frac {\sqrt {7+2 \sqrt {14}}-2 \sqrt {3-2 x}}{\sqrt {2 \sqrt {14}-7}}\right )}{318603459702399434752}-\frac {11275 \sqrt {\frac {1}{2} \left (7+2 \sqrt {14}\right )} \left (9756589235+2148932869 \sqrt {14}\right ) \text {ArcTan}\left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {2 \sqrt {14}-7}}\right )}{318603459702399434752}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}+\frac {451 (14627273 x+28962039)}{283351498752 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}+\frac {451 (998691 x+811091)}{10119696384 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}+\frac {41 (5677637 x+3436375)}{5059848192 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}+\frac {41 (92875 x+47471)}{90354432 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}+\frac {5 (47471 x+21409)}{6453888 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}+\frac {21409 x+8477}{691488 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}+\frac {173 x+53}{7056 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}+\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}+\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \sqrt {\frac {1}{2} \left (2 \sqrt {14}-7\right )} \log \left (-2 x-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}+\sqrt {14}+3\right )}{637206919404798869504}-\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \sqrt {\frac {1}{2} \left (2 \sqrt {14}-7\right )} \log \left (-2 x+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}+\sqrt {14}+3\right )}{637206919404798869504} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 210
Rule 632
Rule 642
Rule 648
Rule 754
Rule 836
Rule 840
Rule 842
Rule 1183
Rubi steps
\begin {align*} \int \frac {1}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {\int \frac {1680-1484 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^9} \, dx}{1764}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {\int \frac {2534672-3322984 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^8} \, dx}{2765952}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {\int \frac {3218135760-5287166640 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^7} \, dx}{3794886144}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {\int \frac {3218122918080-6729253503840 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^6} \, dx}{4462786105344}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {\int \frac {2223971291223360-6819728658120000 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^5} \, dx}{4373530383237120}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {\int \frac {602017891719552000-5205664113141824640 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^4} \, dx}{3428847820457902080}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {\int \frac {-644013851165157876480-2602338158011857027840 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^3} \, dx}{2016162518429246423040}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {\int \frac {-781280013553524600192000-460008659488539446208000 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^2} \, dx}{790335707224264597831680}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-209865664941946247912832000+324150102079841867727744000 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )} \, dx}{154905798615955861175009280}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-2327225523695253718758144000+1105437952711266214715136000 x}{(3-2 x)^{19/2} \left (1+x+2 x^2\right )} \, dx}{4337362361246764112900259840}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-20828680094984562179495424000-2676274378513417586741760000 x}{(3-2 x)^{17/2} \left (1+x+2 x^2\right )} \, dx}{121446146114909395161207275520}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-161276892002849662262479872000-99372366651018754238432256000 x}{(3-2 x)^{15/2} \left (1+x+2 x^2\right )} \, dx}{3400492091217463064513803714560}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-1091470402720759789622974464000-1241341767917511174480513024000 x}{(3-2 x)^{13/2} \left (1+x+2 x^2\right )} \, dx}{95213778554088965806386504007680}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-6249079685931055968022769664000-11813932218388106205374976000000 x}{(3-2 x)^{11/2} \left (1+x+2 x^2\right )} \, dx}{2665985799514491042578822112215040}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-26364773050672235333432205312000-95879912054052861104340934656000 x}{(3-2 x)^{9/2} \left (1+x+2 x^2\right )} \, dx}{74647602386405749192207019142021120}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-19158360297272160458775773184000-680738564527006107959774429184000 x}{(3-2 x)^{7/2} \left (1+x+2 x^2\right )} \, dx}{2090132866819360977381796535976591360}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {1208210246675834932249342672896000-4161064828351125289593749667840000 x}{(3-2 x)^{5/2} \left (1+x+2 x^2\right )} \, dx}{58523720270942107366690303007344558080}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {17987811630108930037182240718848000-20133547983403412008565127315456000 x}{(3-2 x)^{3/2} \left (1+x+2 x^2\right )} \, dx}{1638664167586379006267328484205647626240}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {184169589007678264314588180381696000-48850041379984751902661801017344000 x}{\sqrt {3-2 x} \left (1+x+2 x^2\right )} \, dx}{45882596692418612175485197557758133534720}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\text {Subst}\left (\int \frac {-221789053875402272921190957711360000-48850041379984751902661801017344000 x^2}{28-14 x^2+2 x^4} \, dx,x,\sqrt {3-2 x}\right )}{22941298346209306087742598778879066767360}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\text {Subst}\left (\int \frac {-221789053875402272921190957711360000 \sqrt {7+2 \sqrt {14}}-\left (-221789053875402272921190957711360000+48850041379984751902661801017344000 \sqrt {14}\right ) x}{\sqrt {14}-\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{91765193384837224350970395115516267069440 \sqrt {14 \left (7+2 \sqrt {14}\right )}}+\frac {\text {Subst}\left (\int \frac {-221789053875402272921190957711360000 \sqrt {7+2 \sqrt {14}}+\left (-221789053875402272921190957711360000+48850041379984751902661801017344000 \sqrt {14}\right ) x}{\sqrt {14}+\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{91765193384837224350970395115516267069440 \sqrt {14 \left (7+2 \sqrt {14}\right )}}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\left (11275 \left (9756589235-2148932869 \sqrt {14}\right )\right ) \text {Subst}\left (\int \frac {-\sqrt {7+2 \sqrt {14}}+2 x}{\sqrt {14}-\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{91029559914971267072 \sqrt {14 \left (7+2 \sqrt {14}\right )}}-\frac {\left (11275 \left (9756589235-2148932869 \sqrt {14}\right )\right ) \text {Subst}\left (\int \frac {\sqrt {7+2 \sqrt {14}}+2 x}{\sqrt {14}+\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{91029559914971267072 \sqrt {14 \left (7+2 \sqrt {14}\right )}}-\frac {\left (11275 \left (30085060166+9756589235 \sqrt {14}\right )\right ) \text {Subst}\left (\int \frac {1}{\sqrt {14}-\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{1274413838809597739008}-\frac {\left (11275 \left (30085060166+9756589235 \sqrt {14}\right )\right ) \text {Subst}\left (\int \frac {1}{\sqrt {14}+\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{1274413838809597739008}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \log \left (3+\sqrt {14}-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{91029559914971267072 \sqrt {14 \left (7+2 \sqrt {14}\right )}}-\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \log \left (3+\sqrt {14}+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{91029559914971267072 \sqrt {14 \left (7+2 \sqrt {14}\right )}}+\frac {\left (11275 \left (30085060166+9756589235 \sqrt {14}\right )\right ) \text {Subst}\left (\int \frac {1}{7-2 \sqrt {14}-x^2} \, dx,x,-\sqrt {7+2 \sqrt {14}}+2 \sqrt {3-2 x}\right )}{637206919404798869504}+\frac {\left (11275 \left (30085060166+9756589235 \sqrt {14}\right )\right ) \text {Subst}\left (\int \frac {1}{7-2 \sqrt {14}-x^2} \, dx,x,\sqrt {7+2 \sqrt {14}}+2 \sqrt {3-2 x}\right )}{637206919404798869504}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {11275 \sqrt {\frac {1}{2} \left (7+2 \sqrt {14}\right )} \left (9756589235+2148932869 \sqrt {14}\right ) \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}-2 \sqrt {3-2 x}}{\sqrt {-7+2 \sqrt {14}}}\right )}{318603459702399434752}-\frac {11275 \sqrt {\frac {1}{2} \left (7+2 \sqrt {14}\right )} \left (9756589235+2148932869 \sqrt {14}\right ) \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}+2 \sqrt {3-2 x}}{\sqrt {-7+2 \sqrt {14}}}\right )}{318603459702399434752}+\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \log \left (3+\sqrt {14}-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{91029559914971267072 \sqrt {14 \left (7+2 \sqrt {14}\right )}}-\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \log \left (3+\sqrt {14}+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{91029559914971267072 \sqrt {14 \left (7+2 \sqrt {14}\right )}}\\ \end {align*}
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Mathematica [C] Result contains complex when optimal does not.
time = 7.15, size = 253, normalized size = 0.39 \begin {gather*} \frac {\frac {14 \left (-4884417100172357749737+205702452014540322797289 x+111926768697602999806116 x^2+1362587089603925431664856 x^3-809990362095044210054958 x^4+3673303058277822225386926 x^5-8685973988079840377705700 x^6+10718131725916893151555068 x^7-27246604251076689552043953 x^8+41613884937255303086792337 x^9-59791102681494117572149176 x^{10}+102031573634317834547976132 x^{11}-133312541377246386115890240 x^{12}+172649692294614969274168896 x^{13}-229408132984166521977166336 x^{14}+258819256815163249845447936 x^{15}-282644664539994827031006720 x^{16}+304010591010966811155955200 x^{17}-287279159180291305208156160 x^{18}+253788172995391086570485760 x^{19}-216634228326470609547509760 x^{20}+162290307223249502039654400 x^{21}-106701725825102321939251200 x^{22}+65360120291258796757811200 x^{23}-33969890064381284111155200 x^{24}+12365045055896811105484800 x^{25}-2621948941596237063782400 x^{26}+240031204937714427494400 x^{27}\right )}{(3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}-426093525 \sqrt {2293002953699236822393+30540258843957888971 i \sqrt {7}} \tan ^{-1}\left (\frac {1}{2} \sqrt {-1-\frac {i}{\sqrt {7}}} \sqrt {3-2 x}\right )-426093525 \sqrt {2293002953699236822393-30540258843957888971 i \sqrt {7}} \tan ^{-1}\left (\frac {1}{2} \sqrt {-1+\frac {i}{\sqrt {7}}} \sqrt {3-2 x}\right )}{12040343345613377038712832} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.91, size = 550, normalized size = 0.85 Too large to display
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 1563 vs.
\(2 (491) = 982\).
time = 1.73, size = 1563, normalized size = 2.41 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 1000 vs.
\(2 (491) = 982\).
time = 1.75, size = 1000, normalized size = 1.54 \begin {gather*} -\frac {11275}{142734349946674946768896} \, \sqrt {7} {\left (6446798607 \cdot 14^{\frac {3}{4}} \sqrt {7} {\left (\sqrt {14} + 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 2148932869 \cdot 14^{\frac {3}{4}} \sqrt {7} {\left (\sqrt {14} - 4\right )} \sqrt {-2 \, \sqrt {14} + 8} - 15042530083 \cdot 14^{\frac {3}{4}} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} + 4\right )} - 45127590249 \cdot 14^{\frac {3}{4}} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} - 4\right )} + 78052713880 \cdot 14^{\frac {1}{4}} \sqrt {7} \sqrt {-2 \, \sqrt {14} + 8} - 546368997160 \cdot 14^{\frac {1}{4}} \sqrt {2 \, \sqrt {14} + 8}\right )} \arctan \left (\frac {14^{\frac {3}{4}} {\left (14^{\frac {1}{4}} \sqrt {\frac {1}{2}} \sqrt {\sqrt {14} + 4} + 2 \, \sqrt {-2 \, x + 3}\right )}}{28 \, \sqrt {-\frac {1}{8} \, \sqrt {14} + \frac {1}{2}}}\right ) - \frac {11275}{142734349946674946768896} \, \sqrt {7} {\left (6446798607 \cdot 14^{\frac {3}{4}} \sqrt {7} {\left (\sqrt {14} + 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 2148932869 \cdot 14^{\frac {3}{4}} \sqrt {7} {\left (\sqrt {14} - 4\right )} \sqrt {-2 \, \sqrt {14} + 8} - 15042530083 \cdot 14^{\frac {3}{4}} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} + 4\right )} - 45127590249 \cdot 14^{\frac {3}{4}} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} - 4\right )} + 78052713880 \cdot 14^{\frac {1}{4}} \sqrt {7} \sqrt {-2 \, \sqrt {14} + 8} - 546368997160 \cdot 14^{\frac {1}{4}} \sqrt {2 \, \sqrt {14} + 8}\right )} \arctan \left (-\frac {14^{\frac {3}{4}} {\left (14^{\frac {1}{4}} \sqrt {\frac {1}{2}} \sqrt {\sqrt {14} + 4} - 2 \, \sqrt {-2 \, x + 3}\right )}}{28 \, \sqrt {-\frac {1}{8} \, \sqrt {14} + \frac {1}{2}}}\right ) - \frac {11275}{285468699893349893537792} \, \sqrt {7} {\left (2148932869 \cdot 14^{\frac {3}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} + 4\right )} + 6446798607 \cdot 14^{\frac {3}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} - 4\right )} + 45127590249 \cdot 14^{\frac {3}{4}} {\left (\sqrt {14} + 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 15042530083 \cdot 14^{\frac {3}{4}} {\left (\sqrt {14} - 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 78052713880 \cdot 14^{\frac {1}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} + 546368997160 \cdot 14^{\frac {1}{4}} \sqrt {-2 \, \sqrt {14} + 8}\right )} \log \left (14^{\frac {1}{4}} \sqrt {\frac {1}{2}} \sqrt {-2 \, x + 3} \sqrt {\sqrt {14} + 4} - 2 \, x + \sqrt {14} + 3\right ) + \frac {11275}{285468699893349893537792} \, \sqrt {7} {\left (2148932869 \cdot 14^{\frac {3}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} + 4\right )} + 6446798607 \cdot 14^{\frac {3}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} - 4\right )} + 45127590249 \cdot 14^{\frac {3}{4}} {\left (\sqrt {14} + 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 15042530083 \cdot 14^{\frac {3}{4}} {\left (\sqrt {14} - 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 78052713880 \cdot 14^{\frac {1}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} + 546368997160 \cdot 14^{\frac {1}{4}} \sqrt {-2 \, \sqrt {14} + 8}\right )} \log \left (-14^{\frac {1}{4}} \sqrt {\frac {1}{2}} \sqrt {-2 \, x + 3} \sqrt {\sqrt {14} + 4} - 2 \, x + \sqrt {14} + 3\right ) + \frac {232787883652335 \, {\left (2 \, x - 3\right )}^{17} \sqrt {-2 \, x + 3} + 13820106668010555 \, {\left (2 \, x - 3\right )}^{16} \sqrt {-2 \, x + 3} + 389618236717151904 \, {\left (2 \, x - 3\right )}^{15} \sqrt {-2 \, x + 3} + 6925854690067471092 \, {\left (2 \, x - 3\right )}^{14} \sqrt {-2 \, x + 3} + 86924717622268515682 \, {\left (2 \, x - 3\right )}^{13} \sqrt {-2 \, x + 3} + 817308030405306394458 \, {\left (2 \, x - 3\right )}^{12} \sqrt {-2 \, x + 3} + 5960699611609964201316 \, {\left (2 \, x - 3\right )}^{11} \sqrt {-2 \, x + 3} + 34438539253455396724476 \, {\left (2 \, x - 3\right )}^{10} \sqrt {-2 \, x + 3} + 159569809573892673649239 \, {\left (2 \, x - 3\right )}^{9} \sqrt {-2 \, x + 3} + 596312099501239401271299 \, {\left (2 \, x - 3\right )}^{8} \sqrt {-2 \, x + 3} + 1797250621001927736488676 \, {\left (2 \, x - 3\right )}^{7} \sqrt {-2 \, x + 3} + 4343978582610098069631672 \, {\left (2 \, x - 3\right )}^{6} \sqrt {-2 \, x + 3} + 8317212692450176764092592 \, {\left (2 \, x - 3\right )}^{5} \sqrt {-2 \, x + 3} + 12350951282904546626644288 \, {\left (2 \, x - 3\right )}^{4} \sqrt {-2 \, x + 3} + 13738697725192288735303872 \, {\left (2 \, x - 3\right )}^{3} \sqrt {-2 \, x + 3} + 10788479661863702869789824 \, {\left (2 \, x - 3\right )}^{2} \sqrt {-2 \, x + 3} - 5340653236079401357791744 \, {\left (-2 \, x + 3\right )}^{\frac {3}{2}} + 1255138952440667471476992 \, \sqrt {-2 \, x + 3}}{204816509808685350912 \, {\left ({\left (2 \, x - 3\right )}^{2} + 14 \, x - 7\right )}^{9}} + \frac {235862511885 \, {\left (2 \, x - 3\right )}^{9} - 107316677325 \, {\left (2 \, x - 3\right )}^{8} + 80348352084 \, {\left (2 \, x - 3\right )}^{7} - 64554208290 \, {\left (2 \, x - 3\right )}^{6} + 49954696792 \, {\left (2 \, x - 3\right )}^{5} - 35035280280 \, {\left (2 \, x - 3\right )}^{4} + 21058773120 \, {\left (2 \, x - 3\right )}^{3} - 10093321056 \, {\left (2 \, x - 3\right )}^{2} + 6831901440 \, x - 10859127552}{3280733202692679552 \, {\left (2 \, x - 3\right )}^{9} \sqrt {-2 \, x + 3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.56, size = 567, normalized size = 0.88 \begin {gather*} \frac {\frac {184192\,{\left (2\,x-3\right )}^2}{47481}-\frac {18944\,x}{2261}-\frac {15552\,{\left (2\,x-3\right )}^3}{4199}+\frac {5666272\,{\left (2\,x-3\right )}^4}{1440257}-\frac {63490768\,{\left (2\,x-3\right )}^5}{12962313}+\frac {533495672\,{\left (2\,x-3\right )}^6}{70572593}-\frac {1111521492\,{\left (2\,x-3\right )}^7}{70572593}+\frac {78007323158\,{\left (2\,x-3\right )}^8}{1482024453}-\frac {250239440467\,{\left (2\,x-3\right )}^9}{494008151}+\frac {1118693654785651073\,{\left (2\,x-3\right )}^{10}}{453254454575104}+\frac {1624300450152249301\,{\left (2\,x-3\right )}^{11}}{97125954551808}+\frac {35048653520674948897\,{\left (2\,x-3\right )}^{12}}{906508909150208}+\frac {95527511967437577915\,{\left (2\,x-3\right )}^{13}}{1813017818300416}+\frac {5640662999731415610547\,{\left (2\,x-3\right )}^{14}}{114220122552926208}+\frac {1737142288764447500149\,{\left (2\,x-3\right )}^{15}}{50764498912411648}+\frac {12971210667229097601055\,{\left (2\,x-3\right )}^{16}}{710702984773763072}+\frac {32723441206946795665235\,{\left (2\,x-3\right )}^{17}}{4264217908642578432}+\frac {102645797034777710681325\,{\left (2\,x-3\right )}^{18}}{39799367147330732032}+\frac {1460931787430200665315\,{\left (2\,x-3\right )}^{19}}{2094703534070038528}+\frac {687618468821894139745\,{\left (2\,x-3\right )}^{20}}{4528256169239642112}+\frac {39968995676603847725\,{\left (2\,x-3\right )}^{21}}{1509418723079880704}+\frac {5940132943613849875\,{\left (2\,x-3\right )}^{22}}{1625527855624486912}+\frac {5717978503620010375\,{\left (2\,x-3\right )}^{23}}{14629750700620382208}+\frac {178056995818325525\,{\left (2\,x-3\right )}^{24}}{5689347494685704192}+\frac {179665281323275\,{\left (2\,x-3\right )}^{25}}{101595490976530432}+\frac {1433237383402275\,{\left (2\,x-3\right )}^{26}}{22757389978742816768}+\frac {24229218097975\,{\left (2\,x-3\right )}^{27}}{22757389978742816768}+\frac {37120}{2261}}{20661046784\,{\left (3-2\,x\right )}^{19/2}-92974710528\,{\left (3-2\,x\right )}^{21/2}+199231522560\,{\left (3-2\,x\right )}^{23/2}-270069397248\,{\left (3-2\,x\right )}^{25/2}+259475340096\,{\left (3-2\,x\right )}^{27/2}-187609683744\,{\left (3-2\,x\right )}^{29/2}+105782451264\,{\left (3-2\,x\right )}^{31/2}-47554666992\,{\left (3-2\,x\right )}^{33/2}+17278167438\,{\left (3-2\,x\right )}^{35/2}-5111496103\,{\left (3-2\,x\right )}^{37/2}+1234154817\,{\left (3-2\,x\right )}^{39/2}-242625852\,{\left (3-2\,x\right )}^{41/2}+38550456\,{\left (3-2\,x\right )}^{43/2}-4883634\,{\left (3-2\,x\right )}^{45/2}+482454\,{\left (3-2\,x\right )}^{47/2}-35868\,{\left (3-2\,x\right )}^{49/2}+1890\,{\left (3-2\,x\right )}^{51/2}-63\,{\left (3-2\,x\right )}^{53/2}+{\left (3-2\,x\right )}^{55/2}}-\frac {\mathrm {atan}\left (\frac {\sqrt {-2293002953699236822393-\sqrt {7}\,30540258843957888971{}\mathrm {i}}\,\sqrt {3-2\,x}\,43774618035829144330316520640625{}\mathrm {i}}{330008698047761583560870082619263806430093600589158123831296\,\left (\frac {803365829195061345550676106938401175484375}{23572049860554398825776434472804557602149542899225580273664}+\frac {\sqrt {7}\,427090967094607473872427449424977178671875{}\mathrm {i}}{165004349023880791780435041309631903215046800294579061915648}\right )}+\frac {43774618035829144330316520640625\,\sqrt {7}\,\sqrt {-2293002953699236822393-\sqrt {7}\,30540258843957888971{}\mathrm {i}}\,\sqrt {3-2\,x}}{330008698047761583560870082619263806430093600589158123831296\,\left (\frac {803365829195061345550676106938401175484375}{23572049860554398825776434472804557602149542899225580273664}+\frac {\sqrt {7}\,427090967094607473872427449424977178671875{}\mathrm {i}}{165004349023880791780435041309631903215046800294579061915648}\right )}\right )\,\sqrt {-2293002953699236822393-\sqrt {7}\,30540258843957888971{}\mathrm {i}}\,11275{}\mathrm {i}}{318603459702399434752}+\frac {\mathrm {atan}\left (\frac {\sqrt {-2293002953699236822393+\sqrt {7}\,30540258843957888971{}\mathrm {i}}\,\sqrt {3-2\,x}\,43774618035829144330316520640625{}\mathrm {i}}{330008698047761583560870082619263806430093600589158123831296\,\left (-\frac {803365829195061345550676106938401175484375}{23572049860554398825776434472804557602149542899225580273664}+\frac {\sqrt {7}\,427090967094607473872427449424977178671875{}\mathrm {i}}{165004349023880791780435041309631903215046800294579061915648}\right )}-\frac {43774618035829144330316520640625\,\sqrt {7}\,\sqrt {-2293002953699236822393+\sqrt {7}\,30540258843957888971{}\mathrm {i}}\,\sqrt {3-2\,x}}{330008698047761583560870082619263806430093600589158123831296\,\left (-\frac {803365829195061345550676106938401175484375}{23572049860554398825776434472804557602149542899225580273664}+\frac {\sqrt {7}\,427090967094607473872427449424977178671875{}\mathrm {i}}{165004349023880791780435041309631903215046800294579061915648}\right )}\right )\,\sqrt {-2293002953699236822393+\sqrt {7}\,30540258843957888971{}\mathrm {i}}\,11275{}\mathrm {i}}{318603459702399434752} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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