Optimal. Leaf size=407 \[ -\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38225}{240945152 \sqrt {3-2 x}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {5 \sqrt {\frac {1}{2} \left (149046503977+40815066112 \sqrt {14}\right )} \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}-2 \sqrt {3-2 x}}{\sqrt {-7+2 \sqrt {14}}}\right )}{3373232128}-\frac {5 \sqrt {\frac {1}{2} \left (149046503977+40815066112 \sqrt {14}\right )} \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}+2 \sqrt {3-2 x}}{\sqrt {-7+2 \sqrt {14}}}\right )}{3373232128}+\frac {5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \sqrt {14}\right )} \log \left (3+\sqrt {14}-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{6746464256}-\frac {5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \sqrt {14}\right )} \log \left (3+\sqrt {14}+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{6746464256} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.40, antiderivative size = 407, normalized size of antiderivative = 1.00, number of steps
used = 19, 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 {5 \sqrt {\frac {1}{2} \left (149046503977+40815066112 \sqrt {14}\right )} \text {ArcTan}\left (\frac {\sqrt {7+2 \sqrt {14}}-2 \sqrt {3-2 x}}{\sqrt {2 \sqrt {14}-7}}\right )}{3373232128}-\frac {5 \sqrt {\frac {1}{2} \left (149046503977+40815066112 \sqrt {14}\right )} \text {ArcTan}\left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {2 \sqrt {14}-7}}\right )}{3373232128}+\frac {x}{28 (3-2 x)^{9/2} \left (2 x^2+x+1\right )^4}+\frac {5 (4377 x+3049)}{153664 (3-2 x)^{9/2} \left (2 x^2+x+1\right )}+\frac {3049 x+1387}{32928 (3-2 x)^{9/2} \left (2 x^2+x+1\right )^2}+\frac {73 x+23}{1176 (3-2 x)^{9/2} \left (2 x^2+x+1\right )^3}-\frac {38225}{240945152 \sqrt {3-2 x}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {19255}{395136 (3-2 x)^{9/2}}+\frac {5 \sqrt {\frac {1}{2} \left (40815066112 \sqrt {14}-149046503977\right )} \log \left (-2 x-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}+\sqrt {14}+3\right )}{6746464256}-\frac {5 \sqrt {\frac {1}{2} \left (40815066112 \sqrt {14}-149046503977\right )} \log \left (-2 x+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}+\sqrt {14}+3\right )}{6746464256} \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)^{11/2} \left (1+x+2 x^2\right )^5} \, dx &=\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {1}{784} \int \frac {700-644 x}{(3-2 x)^{11/2} \left (1+x+2 x^2\right )^4} \, dx\\ &=\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {\int \frac {325752-543704 x}{(3-2 x)^{11/2} \left (1+x+2 x^2\right )^3} \, dx}{460992}\\ &=\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {\int \frac {54660480-250993680 x}{(3-2 x)^{11/2} \left (1+x+2 x^2\right )^2} \, dx}{180708864}\\ &=\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-25503229920-55488454560 x}{(3-2 x)^{11/2} \left (1+x+2 x^2\right )} \, dx}{35418937344}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-93048930240-434943647040 x}{(3-2 x)^{9/2} \left (1+x+2 x^2\right )} \, dx}{991730245632}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {125495852160-2981857603200 x}{(3-2 x)^{7/2} \left (1+x+2 x^2\right )} \, dx}{27768446877696}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {6967682023680-17389162210560 x}{(3-2 x)^{5/2} \left (1+x+2 x^2\right )} \, dx}{777516512575488}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {90519780610560-76464245168640 x}{(3-2 x)^{3/2} \left (1+x+2 x^2\right )} \, dx}{21770462352113664}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38225}{240945152 \sqrt {3-2 x}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {877086735221760-96706348569600 x}{\sqrt {3-2 x} \left (1+x+2 x^2\right )} \, dx}{609572945859182592}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38225}{240945152 \sqrt {3-2 x}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\text {Subst}\left (\int \frac {-1464054424734720-96706348569600 x^2}{28-14 x^2+2 x^4} \, dx,x,\sqrt {3-2 x}\right )}{304786472929591296}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38225}{240945152 \sqrt {3-2 x}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {\text {Subst}\left (\int \frac {-1464054424734720 \sqrt {7+2 \sqrt {14}}-\left (-1464054424734720+96706348569600 \sqrt {14}\right ) x}{\sqrt {14}-\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{1219145891718365184 \sqrt {14 \left (7+2 \sqrt {14}\right )}}+\frac {\text {Subst}\left (\int \frac {-1464054424734720 \sqrt {7+2 \sqrt {14}}+\left (-1464054424734720+96706348569600 \sqrt {14}\right ) x}{\sqrt {14}+\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{1219145891718365184 \sqrt {14 \left (7+2 \sqrt {14}\right )}}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38225}{240945152 \sqrt {3-2 x}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}-\frac {\left (5 \left (107030+115739 \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 )}{13492928512}-\frac {\left (5 \left (107030+115739 \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 )}{13492928512}+\frac {\left (5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \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 )}{6746464256}-\frac {\left (5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \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 )}{6746464256}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38225}{240945152 \sqrt {3-2 x}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \sqrt {14}\right )} \log \left (3+\sqrt {14}-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{6746464256}-\frac {5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \sqrt {14}\right )} \log \left (3+\sqrt {14}+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{6746464256}+\frac {\left (5 \left (107030+115739 \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 )}{6746464256}+\frac {\left (5 \left (107030+115739 \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 )}{6746464256}\\ &=-\frac {19255}{395136 (3-2 x)^{9/2}}-\frac {462025}{30118144 (3-2 x)^{7/2}}-\frac {38491}{8605184 (3-2 x)^{5/2}}-\frac {141045}{120472576 (3-2 x)^{3/2}}-\frac {38225}{240945152 \sqrt {3-2 x}}+\frac {x}{28 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}+\frac {23+73 x}{1176 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^3}+\frac {1387+3049 x}{32928 (3-2 x)^{9/2} \left (1+x+2 x^2\right )^2}+\frac {5 (3049+4377 x)}{153664 (3-2 x)^{9/2} \left (1+x+2 x^2\right )}+\frac {5 \sqrt {298093007954+81630132224 \sqrt {14}} \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}-2 \sqrt {3-2 x}}{\sqrt {-7+2 \sqrt {14}}}\right )}{6746464256}-\frac {5 \sqrt {298093007954+81630132224 \sqrt {14}} \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}+2 \sqrt {3-2 x}}{\sqrt {-7+2 \sqrt {14}}}\right )}{6746464256}+\frac {5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \sqrt {14}\right )} \log \left (3+\sqrt {14}-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{6746464256}-\frac {5 \sqrt {\frac {1}{2} \left (-149046503977+40815066112 \sqrt {14}\right )} \log \left (3+\sqrt {14}+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{6746464256}\\ \end {align*}
________________________________________________________________________________________
Mathematica [C] Result contains complex when optimal does not.
time = 4.41, size = 178, normalized size = 0.44 \begin {gather*} \frac {-\frac {14 \left (40289347-429812744 x+135202154 x^2-1073855156 x^3+1627773523 x^4-1470758860 x^5+2888625656 x^6-3106712560 x^7+2343370048 x^8-2443779648 x^9+1873554048 x^{10}-677249280 x^{11}+88070400 x^{12}\right )}{(3-2 x)^{9/2} \left (1+x+2 x^2\right )^4}-45 \sqrt {149046503977+12577271771 i \sqrt {7}} \tan ^{-1}\left (\frac {1}{2} \sqrt {-1-\frac {i}{\sqrt {7}}} \sqrt {3-2 x}\right )-45 \sqrt {149046503977-12577271771 i \sqrt {7}} \tan ^{-1}\left (\frac {1}{2} \sqrt {-1+\frac {i}{\sqrt {7}}} \sqrt {3-2 x}\right )}{30359089152} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.89, size = 415, normalized size = 1.02 Too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 957 vs.
\(2 (298) = 596\).
time = 1.32, size = 957, normalized size = 2.35 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 795 vs.
\(2 (298) = 596\).
time = 1.28, size = 795, normalized size = 1.95 \begin {gather*} -\frac {5}{1511207993344} \, \sqrt {7} {\left (22935 \cdot 14^{\frac {3}{4}} \sqrt {7} {\left (\sqrt {14} + 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 7645 \cdot 14^{\frac {3}{4}} \sqrt {7} {\left (\sqrt {14} - 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 53515 \cdot 14^{\frac {3}{4}} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} + 4\right )} + 160545 \cdot 14^{\frac {3}{4}} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} - 4\right )} + 925912 \cdot 14^{\frac {1}{4}} \sqrt {7} \sqrt {-2 \, \sqrt {14} + 8} + 6481384 \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 {5}{1511207993344} \, \sqrt {7} {\left (22935 \cdot 14^{\frac {3}{4}} \sqrt {7} {\left (\sqrt {14} + 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 7645 \cdot 14^{\frac {3}{4}} \sqrt {7} {\left (\sqrt {14} - 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 53515 \cdot 14^{\frac {3}{4}} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} + 4\right )} + 160545 \cdot 14^{\frac {3}{4}} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} - 4\right )} + 925912 \cdot 14^{\frac {1}{4}} \sqrt {7} \sqrt {-2 \, \sqrt {14} + 8} + 6481384 \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 {5}{3022415986688} \, \sqrt {7} {\left (7645 \cdot 14^{\frac {3}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} + 4\right )} + 22935 \cdot 14^{\frac {3}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} - 4\right )} - 160545 \cdot 14^{\frac {3}{4}} {\left (\sqrt {14} + 4\right )} \sqrt {-2 \, \sqrt {14} + 8} - 53515 \cdot 14^{\frac {3}{4}} {\left (\sqrt {14} - 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 925912 \cdot 14^{\frac {1}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} - 6481384 \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 {5}{3022415986688} \, \sqrt {7} {\left (7645 \cdot 14^{\frac {3}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} + 4\right )} + 22935 \cdot 14^{\frac {3}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} {\left (\sqrt {14} - 4\right )} - 160545 \cdot 14^{\frac {3}{4}} {\left (\sqrt {14} + 4\right )} \sqrt {-2 \, \sqrt {14} + 8} - 53515 \cdot 14^{\frac {3}{4}} {\left (\sqrt {14} - 4\right )} \sqrt {-2 \, \sqrt {14} + 8} + 925912 \cdot 14^{\frac {1}{4}} \sqrt {7} \sqrt {2 \, \sqrt {14} + 8} - 6481384 \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 {1578405 \, {\left (2 \, x - 3\right )}^{7} \sqrt {-2 \, x + 3} + 37939930 \, {\left (2 \, x - 3\right )}^{6} \sqrt {-2 \, x + 3} + 400127266 \, {\left (2 \, x - 3\right )}^{5} \sqrt {-2 \, x + 3} + 2394090608 \, {\left (2 \, x - 3\right )}^{4} \sqrt {-2 \, x + 3} + 8763772549 \, {\left (2 \, x - 3\right )}^{3} \sqrt {-2 \, x + 3} + 19602865030 \, {\left (2 \, x - 3\right )}^{2} \sqrt {-2 \, x + 3} - 24778425644 \, {\left (-2 \, x + 3\right )}^{\frac {3}{2}} + 13623638952 \, \sqrt {-2 \, x + 3}}{5059848192 \, {\left ({\left (2 \, x - 3\right )}^{2} + 14 \, x - 7\right )}^{4}} + \frac {9090 \, {\left (2 \, x - 3\right )}^{4} - 3885 \, {\left (2 \, x - 3\right )}^{3} + 2394 \, {\left (2 \, x - 3\right )}^{2} - 2520 \, x + 4172}{59295096 \, {\left (2 \, x - 3\right )}^{4} \sqrt {-2 \, x + 3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.47, size = 343, normalized size = 0.84 \begin {gather*} -\frac {\frac {272\,x}{441}-\frac {164\,{\left (2\,x-3\right )}^2}{441}+\frac {1966\,{\left (2\,x-3\right )}^3}{3087}-\frac {9091\,{\left (2\,x-3\right )}^4}{3087}-\frac {32070727\,{\left (2\,x-3\right )}^5}{5531904}-\frac {41014777\,{\left (2\,x-3\right )}^6}{11063808}-\frac {141921511\,{\left (2\,x-3\right )}^7}{154893312}+\frac {23262655\,{\left (2\,x-3\right )}^8}{309786624}+\frac {1571659\,{\left (2\,x-3\right )}^9}{15059072}+\frac {468427\,{\left (2\,x-3\right )}^{10}}{17210368}+\frac {394105\,{\left (2\,x-3\right )}^{11}}{120472576}+\frac {38225\,{\left (2\,x-3\right )}^{12}}{240945152}-\frac {520}{441}}{38416\,{\left (3-2\,x\right )}^{9/2}-76832\,{\left (3-2\,x\right )}^{11/2}+68600\,{\left (3-2\,x\right )}^{13/2}-35672\,{\left (3-2\,x\right )}^{15/2}+11809\,{\left (3-2\,x\right )}^{17/2}-2548\,{\left (3-2\,x\right )}^{19/2}+350\,{\left (3-2\,x\right )}^{21/2}-28\,{\left (3-2\,x\right )}^{23/2}+{\left (3-2\,x\right )}^{25/2}}+\frac {\mathrm {atan}\left (\frac {\sqrt {3-2\,x}\,\sqrt {-149046503977+\sqrt {7}\,12577271771{}\mathrm {i}}\,1572158971375{}\mathrm {i}}{391663056253676053933850624\,\left (-\frac {230036728532618625}{27975932589548289566703616}+\frac {\sqrt {7}\,181960107187971125{}\mathrm {i}}{195831528126838026966925312}\right )}-\frac {1572158971375\,\sqrt {7}\,\sqrt {3-2\,x}\,\sqrt {-149046503977+\sqrt {7}\,12577271771{}\mathrm {i}}}{391663056253676053933850624\,\left (-\frac {230036728532618625}{27975932589548289566703616}+\frac {\sqrt {7}\,181960107187971125{}\mathrm {i}}{195831528126838026966925312}\right )}\right )\,\sqrt {-149046503977+\sqrt {7}\,12577271771{}\mathrm {i}}\,5{}\mathrm {i}}{3373232128}-\frac {\mathrm {atan}\left (\frac {\sqrt {3-2\,x}\,\sqrt {-149046503977-\sqrt {7}\,12577271771{}\mathrm {i}}\,1572158971375{}\mathrm {i}}{391663056253676053933850624\,\left (\frac {230036728532618625}{27975932589548289566703616}+\frac {\sqrt {7}\,181960107187971125{}\mathrm {i}}{195831528126838026966925312}\right )}+\frac {1572158971375\,\sqrt {7}\,\sqrt {3-2\,x}\,\sqrt {-149046503977-\sqrt {7}\,12577271771{}\mathrm {i}}}{391663056253676053933850624\,\left (\frac {230036728532618625}{27975932589548289566703616}+\frac {\sqrt {7}\,181960107187971125{}\mathrm {i}}{195831528126838026966925312}\right )}\right )\,\sqrt {-149046503977-\sqrt {7}\,12577271771{}\mathrm {i}}\,5{}\mathrm {i}}{3373232128} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________