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} \]
[Out]
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Rubi [A]
time = 0.78, 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 (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}+\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 {2 \sqrt {14}-7}}\right )}{318603459702399434752}-\frac {11275 \sqrt {\frac {1}{2} \left (7+2 \sqrt {14}\right )} \left (9756589235+2148932869 \sqrt {14}\right ) \tan ^{-1}\left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {2 \sqrt {14}-7}}\right )}{318603459702399434752} \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 = 6.85, 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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Mathics [F(-1)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Warning: Unable to verify antiderivative.
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Maple [A]
time = 0.91, size = 550, normalized size = 0.85
method | result | size |
derivativedivides | \(\frac {1}{5367029731 \left (3-2 x \right )^{\frac {19}{2}}}+\frac {5}{4802079233 \left (3-2 x \right )^{\frac {17}{2}}}+\frac {73}{23727920916 \left (3-2 x \right )^{\frac {15}{2}}}+\frac {165}{25705247659 \left (3-2 x \right )^{\frac {13}{2}}}+\frac {2365}{221460595216 \left (3-2 x \right )^{\frac {11}{2}}}+\frac {30349}{1993145356944 \left (3-2 x \right )^{\frac {9}{2}}}+\frac {854095}{43406276662336 \left (3-2 x \right )^{\frac {7}{2}}}+\frac {75933}{3100448333024 \left (3-2 x \right )^{\frac {5}{2}}}+\frac {8519225}{260437659974016 \left (3-2 x \right )^{\frac {3}{2}}}+\frac {891605}{12401793332096 \sqrt {3-2 x}}+\frac {-\frac {165574989211387894481 \left (3-2 x \right )^{\frac {23}{2}}}{65536}+\frac {45406001689183688581 \left (3-2 x \right )^{\frac {25}{2}}}{131072}-\frac {43462358811134257841 \left (3-2 x \right )^{\frac {27}{2}}}{1179648}+\frac {192384852501874197 \left (3-2 x \right )^{\frac {29}{2}}}{65536}-\frac {1352841099712333 \left (3-2 x \right )^{\frac {31}{2}}}{8192}+\frac {4606702222670185 \left (3-2 x \right )^{\frac {33}{2}}}{786432}-\frac {25865320405815 \left (3-2 x \right )^{\frac {35}{2}}}{262144}+\frac {544765170330150812273 \sqrt {3-2 x}}{1024}-\frac {3476987783905860258979 \left (3-2 x \right )^{\frac {3}{2}}}{1536}+\frac {9364999706478908741137 \left (3-2 x \right )^{\frac {5}{2}}}{2048}-\frac {23851905772903279054347 \left (3-2 x \right )^{\frac {7}{2}}}{4096}+\frac {192983613795383541041317 \left (3-2 x \right )^{\frac {9}{2}}}{36864}-\frac {57758421475348449750643 \left (3-2 x \right )^{\frac {11}{2}}}{16384}+\frac {60333035869584695411551 \left (3-2 x \right )^{\frac {13}{2}}}{32768}-\frac {149770885083493978040723 \left (3-2 x \right )^{\frac {15}{2}}}{196608}+\frac {66256899944582155696811 \left (3-2 x \right )^{\frac {17}{2}}}{262144}-\frac {17729978841543630405471 \left (3-2 x \right )^{\frac {19}{2}}}{262144}+\frac {2869878271121283060373 \left (3-2 x \right )^{\frac {21}{2}}}{196608}}{86812553324672 \left (\left (3-2 x \right )^{2}-7+14 x \right )^{9}}+\frac {11275 \left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \ln \left (3-2 x +\sqrt {14}+\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right )}{1274413838809597739008}+\frac {11275 \left (-9756589235 \sqrt {14}-\frac {\left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{2}\right ) \arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right )}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}-\frac {11275 \left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \ln \left (3-2 x +\sqrt {14}-\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right )}{1274413838809597739008}-\frac {11275 \left (9756589235 \sqrt {14}+\frac {\left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{2}\right ) \arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right )}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}\) | \(550\) |
default | \(\frac {1}{5367029731 \left (3-2 x \right )^{\frac {19}{2}}}+\frac {5}{4802079233 \left (3-2 x \right )^{\frac {17}{2}}}+\frac {73}{23727920916 \left (3-2 x \right )^{\frac {15}{2}}}+\frac {165}{25705247659 \left (3-2 x \right )^{\frac {13}{2}}}+\frac {2365}{221460595216 \left (3-2 x \right )^{\frac {11}{2}}}+\frac {30349}{1993145356944 \left (3-2 x \right )^{\frac {9}{2}}}+\frac {854095}{43406276662336 \left (3-2 x \right )^{\frac {7}{2}}}+\frac {75933}{3100448333024 \left (3-2 x \right )^{\frac {5}{2}}}+\frac {8519225}{260437659974016 \left (3-2 x \right )^{\frac {3}{2}}}+\frac {891605}{12401793332096 \sqrt {3-2 x}}+\frac {-\frac {165574989211387894481 \left (3-2 x \right )^{\frac {23}{2}}}{65536}+\frac {45406001689183688581 \left (3-2 x \right )^{\frac {25}{2}}}{131072}-\frac {43462358811134257841 \left (3-2 x \right )^{\frac {27}{2}}}{1179648}+\frac {192384852501874197 \left (3-2 x \right )^{\frac {29}{2}}}{65536}-\frac {1352841099712333 \left (3-2 x \right )^{\frac {31}{2}}}{8192}+\frac {4606702222670185 \left (3-2 x \right )^{\frac {33}{2}}}{786432}-\frac {25865320405815 \left (3-2 x \right )^{\frac {35}{2}}}{262144}+\frac {544765170330150812273 \sqrt {3-2 x}}{1024}-\frac {3476987783905860258979 \left (3-2 x \right )^{\frac {3}{2}}}{1536}+\frac {9364999706478908741137 \left (3-2 x \right )^{\frac {5}{2}}}{2048}-\frac {23851905772903279054347 \left (3-2 x \right )^{\frac {7}{2}}}{4096}+\frac {192983613795383541041317 \left (3-2 x \right )^{\frac {9}{2}}}{36864}-\frac {57758421475348449750643 \left (3-2 x \right )^{\frac {11}{2}}}{16384}+\frac {60333035869584695411551 \left (3-2 x \right )^{\frac {13}{2}}}{32768}-\frac {149770885083493978040723 \left (3-2 x \right )^{\frac {15}{2}}}{196608}+\frac {66256899944582155696811 \left (3-2 x \right )^{\frac {17}{2}}}{262144}-\frac {17729978841543630405471 \left (3-2 x \right )^{\frac {19}{2}}}{262144}+\frac {2869878271121283060373 \left (3-2 x \right )^{\frac {21}{2}}}{196608}}{86812553324672 \left (\left (3-2 x \right )^{2}-7+14 x \right )^{9}}+\frac {11275 \left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \ln \left (3-2 x +\sqrt {14}+\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right )}{1274413838809597739008}+\frac {11275 \left (-9756589235 \sqrt {14}-\frac {\left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{2}\right ) \arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right )}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}-\frac {11275 \left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \ln \left (3-2 x +\sqrt {14}-\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right )}{1274413838809597739008}-\frac {11275 \left (9756589235 \sqrt {14}+\frac {\left (18352320711 \sqrt {7+2 \sqrt {14}}\, \sqrt {14}-69111417106 \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{2}\right ) \arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right )}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}\) | \(550\) |
trager | \(\text {Expression too large to display}\) | \(583\) |
risch | \(-\frac {240031204937714427494400 x^{27}-2621948941596237063782400 x^{26}+12365045055896811105484800 x^{25}-33969890064381284111155200 x^{24}+65360120291258796757811200 x^{23}-106701725825102321939251200 x^{22}+162290307223249502039654400 x^{21}-216634228326470609547509760 x^{20}+253788172995391086570485760 x^{19}-287279159180291305208156160 x^{18}+304010591010966811155955200 x^{17}-282644664539994827031006720 x^{16}+258819256815163249845447936 x^{15}-229408132984166521977166336 x^{14}+172649692294614969274168896 x^{13}-133312541377246386115890240 x^{12}+102031573634317834547976132 x^{11}-59791102681494117572149176 x^{10}+41613884937255303086792337 x^{9}-27246604251076689552043953 x^{8}+10718131725916893151555068 x^{7}-8685973988079840377705700 x^{6}+3673303058277822225386926 x^{5}-809990362095044210054958 x^{4}+1362587089603925431664856 x^{3}+111926768697602999806116 x^{2}+205702452014540322797289 x -4884417100172357749737}{860024524686669788479488 \left (2 x^{2}+x +1\right )^{9} \sqrt {3-2 x}\, \left (2 x -3\right )^{9}}-\frac {206922416016525 \ln \left (3-2 x +\sqrt {14}-\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}\, \sqrt {14}}{1274413838809597739008}+\frac {389615613935075 \ln \left (3-2 x +\sqrt {14}-\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{637206919404798869504}-\frac {206922416016525 \arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \left (7+2 \sqrt {14}\right ) \sqrt {14}}{637206919404798869504 \sqrt {-7+2 \sqrt {14}}}+\frac {389615613935075 \arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \left (7+2 \sqrt {14}\right )}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}-\frac {110005543624625 \arctan \left (\frac {2 \sqrt {3-2 x}-\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \sqrt {14}}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}+\frac {206922416016525 \ln \left (3-2 x +\sqrt {14}+\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}\, \sqrt {14}}{1274413838809597739008}-\frac {389615613935075 \ln \left (3-2 x +\sqrt {14}+\sqrt {3-2 x}\, \sqrt {7+2 \sqrt {14}}\right ) \sqrt {7+2 \sqrt {14}}}{637206919404798869504}-\frac {206922416016525 \arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \left (7+2 \sqrt {14}\right ) \sqrt {14}}{637206919404798869504 \sqrt {-7+2 \sqrt {14}}}+\frac {389615613935075 \arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \left (7+2 \sqrt {14}\right )}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}-\frac {110005543624625 \arctan \left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {-7+2 \sqrt {14}}}\right ) \sqrt {14}}{318603459702399434752 \sqrt {-7+2 \sqrt {14}}}\) | \(611\) |
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 = 0.36, size = 1563, normalized size = 2.41
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)]
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 = 0.41, size = 1534, normalized size = 2.37
result too large to display
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
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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