Optimal. Leaf size=319 \[ -\frac {x^2}{20 \left (3+2 x^5\right )^2}+\frac {x^2}{150 \left (3+2 x^5\right )}-\frac {\sqrt {5+\sqrt {5}} \tan ^{-1}\left (\sqrt {\frac {1}{5} \left (5+2 \sqrt {5}\right )}-\frac {2\ 2^{7/10} x}{\sqrt [5]{3} \sqrt {5-\sqrt {5}}}\right )}{250\ 2^{9/10} 3^{3/5}}-\frac {\sqrt {5-\sqrt {5}} \tan ^{-1}\left (\sqrt {\frac {1}{5} \left (5-2 \sqrt {5}\right )}+\frac {2\ 2^{7/10} x}{\sqrt [5]{3} \sqrt {5+\sqrt {5}}}\right )}{250\ 2^{9/10} 3^{3/5}}-\frac {\log \left (\sqrt [5]{3}+\sqrt [5]{2} x\right )}{250\ 2^{2/5} 3^{3/5}}+\frac {\left (1+\sqrt {5}\right ) \log \left (3^{2/5}-\frac {\sqrt [5]{3} \left (1-\sqrt {5}\right ) x}{2^{4/5}}+2^{2/5} x^2\right )}{1000\ 2^{2/5} 3^{3/5}}+\frac {\left (1-\sqrt {5}\right ) \log \left (3^{2/5}-\frac {\sqrt [5]{3} \left (1+\sqrt {5}\right ) x}{2^{4/5}}+2^{2/5} x^2\right )}{1000\ 2^{2/5} 3^{3/5}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.38, antiderivative size = 319, normalized size of antiderivative = 1.00, number of steps
used = 8, number of rules used = 8, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.615, Rules used = {294, 296, 299,
648, 632, 210, 642, 31} \begin {gather*} \frac {\left (1+\sqrt {5}\right ) \log \left (2^{2/5} x^2-\frac {\sqrt [5]{3} \left (1-\sqrt {5}\right ) x}{2^{4/5}}+3^{2/5}\right )}{1000\ 2^{2/5} 3^{3/5}}+\frac {\left (1-\sqrt {5}\right ) \log \left (2^{2/5} x^2-\frac {\sqrt [5]{3} \left (1+\sqrt {5}\right ) x}{2^{4/5}}+3^{2/5}\right )}{1000\ 2^{2/5} 3^{3/5}}+\frac {x^2}{150 \left (2 x^5+3\right )}-\frac {x^2}{20 \left (2 x^5+3\right )^2}-\frac {\log \left (\sqrt [5]{2} x+\sqrt [5]{3}\right )}{250\ 2^{2/5} 3^{3/5}}-\frac {\sqrt {5+\sqrt {5}} \tan ^{-1}\left (\sqrt {\frac {1}{5} \left (5+2 \sqrt {5}\right )}-\frac {2\ 2^{7/10} x}{\sqrt [5]{3} \sqrt {5-\sqrt {5}}}\right )}{250\ 2^{9/10} 3^{3/5}}-\frac {\sqrt {5-\sqrt {5}} \tan ^{-1}\left (\frac {2\ 2^{7/10} x}{\sqrt [5]{3} \sqrt {5+\sqrt {5}}}+\sqrt {\frac {1}{5} \left (5-2 \sqrt {5}\right )}\right )}{250\ 2^{9/10} 3^{3/5}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rule 210
Rule 294
Rule 296
Rule 299
Rule 632
Rule 642
Rule 648
Rubi steps
\begin {align*} \int \frac {x^6}{\left (3+2 x^5\right )^3} \, dx &=-\frac {x^2}{20 \left (3+2 x^5\right )^2}+\frac {1}{10} \int \frac {x}{\left (3+2 x^5\right )^2} \, dx\\ &=-\frac {x^2}{20 \left (3+2 x^5\right )^2}+\frac {x^2}{150 \left (3+2 x^5\right )}+\frac {1}{50} \int \frac {x}{3+2 x^5} \, dx\\ &=-\frac {x^2}{20 \left (3+2 x^5\right )^2}+\frac {x^2}{150 \left (3+2 x^5\right )}-\frac {\int \frac {1}{\sqrt [5]{3}+\sqrt [5]{2} x} \, dx}{250 \sqrt [5]{2} 3^{3/5}}+\frac {\int \frac {\frac {1}{4} \sqrt [5]{3} \left (1-\sqrt {5}\right )-\frac {\left (-1-\sqrt {5}\right ) x}{2\ 2^{4/5}}}{3^{2/5}-\frac {\sqrt [5]{3} \left (1-\sqrt {5}\right ) x}{2^{4/5}}+2^{2/5} x^2} \, dx}{125 \sqrt [5]{2} 3^{3/5}}+\frac {\int \frac {\frac {1}{4} \sqrt [5]{3} \left (1+\sqrt {5}\right )-\frac {\left (-1+\sqrt {5}\right ) x}{2\ 2^{4/5}}}{3^{2/5}-\frac {\sqrt [5]{3} \left (1+\sqrt {5}\right ) x}{2^{4/5}}+2^{2/5} x^2} \, dx}{125 \sqrt [5]{2} 3^{3/5}}\\ &=-\frac {x^2}{20 \left (3+2 x^5\right )^2}+\frac {x^2}{150 \left (3+2 x^5\right )}-\frac {\log \left (\sqrt [5]{3}+\sqrt [5]{2} x\right )}{250\ 2^{2/5} 3^{3/5}}-\frac {\int \frac {1}{3^{2/5}-\frac {\sqrt [5]{3} \left (1-\sqrt {5}\right ) x}{2^{4/5}}+2^{2/5} x^2} \, dx}{100 \sqrt [5]{2} 3^{2/5} \sqrt {5}}+\frac {\int \frac {1}{3^{2/5}-\frac {\sqrt [5]{3} \left (1+\sqrt {5}\right ) x}{2^{4/5}}+2^{2/5} x^2} \, dx}{100 \sqrt [5]{2} 3^{2/5} \sqrt {5}}+\frac {\left (1-\sqrt {5}\right ) \int \frac {-\frac {\sqrt [5]{3} \left (1+\sqrt {5}\right )}{2^{4/5}}+2\ 2^{2/5} x}{3^{2/5}-\frac {\sqrt [5]{3} \left (1+\sqrt {5}\right ) x}{2^{4/5}}+2^{2/5} x^2} \, dx}{1000\ 2^{2/5} 3^{3/5}}+\frac {\left (1+\sqrt {5}\right ) \int \frac {-\frac {\sqrt [5]{3} \left (1-\sqrt {5}\right )}{2^{4/5}}+2\ 2^{2/5} x}{3^{2/5}-\frac {\sqrt [5]{3} \left (1-\sqrt {5}\right ) x}{2^{4/5}}+2^{2/5} x^2} \, dx}{1000\ 2^{2/5} 3^{3/5}}\\ &=-\frac {x^2}{20 \left (3+2 x^5\right )^2}+\frac {x^2}{150 \left (3+2 x^5\right )}-\frac {\log \left (\sqrt [5]{3}+\sqrt [5]{2} x\right )}{250\ 2^{2/5} 3^{3/5}}+\frac {\left (1-\sqrt {5}\right ) \log \left (2\ 3^{2/5}-\sqrt [5]{6} x-\sqrt {5} \sqrt [5]{6} x+2\ 2^{2/5} x^2\right )}{1000\ 2^{2/5} 3^{3/5}}+\frac {\left (1+\sqrt {5}\right ) \log \left (2\ 3^{2/5}-\sqrt [5]{6} x+\sqrt {5} \sqrt [5]{6} x+2\ 2^{2/5} x^2\right )}{1000\ 2^{2/5} 3^{3/5}}-\frac {\text {Subst}\left (\int \frac {1}{-\frac {3^{2/5} \left (5-\sqrt {5}\right )}{2^{3/5}}-x^2} \, dx,x,-\frac {\sqrt [5]{3} \left (1+\sqrt {5}\right )}{2^{4/5}}+2\ 2^{2/5} x\right )}{50 \sqrt [5]{2} 3^{2/5} \sqrt {5}}+\frac {\text {Subst}\left (\int \frac {1}{-\frac {3^{2/5} \left (5+\sqrt {5}\right )}{2^{3/5}}-x^2} \, dx,x,-\frac {\sqrt [5]{3} \left (1-\sqrt {5}\right )}{2^{4/5}}+2\ 2^{2/5} x\right )}{50 \sqrt [5]{2} 3^{2/5} \sqrt {5}}\\ &=-\frac {x^2}{20 \left (3+2 x^5\right )^2}+\frac {x^2}{150 \left (3+2 x^5\right )}-\frac {\tan ^{-1}\left (\frac {\sqrt [5]{3} \left (1+\sqrt {5}\right )-4 \sqrt [5]{2} x}{\sqrt [5]{3} \sqrt {2 \left (5-\sqrt {5}\right )}}\right )}{25\ 2^{9/10} 3^{3/5} \sqrt {5 \left (5-\sqrt {5}\right )}}-\frac {\tan ^{-1}\left (\frac {\sqrt [5]{3} \sqrt {3-\sqrt {5}}+2\ 2^{7/10} x}{\sqrt [5]{3} \sqrt {5+\sqrt {5}}}\right )}{25\ 2^{9/10} 3^{3/5} \sqrt {5 \left (5+\sqrt {5}\right )}}-\frac {\log \left (\sqrt [5]{3}+\sqrt [5]{2} x\right )}{250\ 2^{2/5} 3^{3/5}}+\frac {\left (1-\sqrt {5}\right ) \log \left (2\ 3^{2/5}-\sqrt [5]{6} x-\sqrt {5} \sqrt [5]{6} x+2\ 2^{2/5} x^2\right )}{1000\ 2^{2/5} 3^{3/5}}+\frac {\left (1+\sqrt {5}\right ) \log \left (2\ 3^{2/5}-\sqrt [5]{6} x+\sqrt {5} \sqrt [5]{6} x+2\ 2^{2/5} x^2\right )}{1000\ 2^{2/5} 3^{3/5}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.19, size = 293, normalized size = 0.92 \begin {gather*} \frac {-\frac {300 x^2}{\left (3+2 x^5\right )^2}+\frac {40 x^2}{3+2 x^5}-4 \sqrt [10]{2} 3^{2/5} \sqrt {5-\sqrt {5}} \tan ^{-1}\left (\frac {-3+3 \sqrt {5}+4 \sqrt [5]{2} 3^{4/5} x}{3 \sqrt {2 \left (5+\sqrt {5}\right )}}\right )+4 \sqrt [10]{2} 3^{2/5} \sqrt {5+\sqrt {5}} \tan ^{-1}\left (\frac {-3 \left (1+\sqrt {5}\right )+4 \sqrt [5]{2} 3^{4/5} x}{3 \sqrt {10-2 \sqrt {5}}}\right )-4\ 2^{3/5} 3^{2/5} \log \left (3+\sqrt [5]{2} 3^{4/5} x\right )+2^{3/5} 3^{2/5} \left (1+\sqrt {5}\right ) \log \left (3+\left (\frac {3}{2}\right )^{4/5} \left (-1+\sqrt {5}\right ) x+2^{2/5} 3^{3/5} x^2\right )-2^{3/5} 3^{2/5} \left (-1+\sqrt {5}\right ) \log \left (3-\left (\frac {3}{2}\right )^{4/5} \left (1+\sqrt {5}\right ) x+2^{2/5} 3^{3/5} x^2\right )}{6000} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Mathics [C] Result contains higher order function than in optimal. Order 9 vs. order 3 in
optimal.
time = 2.25, size = 65, normalized size = 0.20 \begin {gather*} \frac {x^2 \left (-9+4 x^5\right )+300 \left (9+12 x^5+4 x^{10}\right ) \text {RootSum}\left [1+105468750000000 \text {\#1}^5\&,\text {Log}\left [x-281250000 \text {\#1}^3\right ] \text {\#1}\&\right ]}{2700+3600 x^5+1200 x^{10}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.10, size = 354, normalized size = 1.11
method | result | size |
risch | \(\frac {\frac {1}{75} x^{7}-\frac {3}{100} x^{2}}{\left (2 x^{5}+3\right )^{2}}+\frac {\left (\munderset {\textit {\_R} =\RootOf \left (2 \textit {\_Z}^{5}+3\right )}{\sum }\frac {\ln \left (-\textit {\_R} +x \right )}{\textit {\_R}^{3}}\right )}{500}\) | \(47\) |
meijerg | \(\frac {108^{\frac {4}{5}} \left (-\frac {x^{2} 3^{\frac {3}{5}} 2^{\frac {2}{5}} \left (-\frac {28 x^{5}}{3}+21\right )}{105 \left (1+\frac {2 x^{5}}{3}\right )^{2}}+\frac {2 \,108^{\frac {1}{5}} x^{2} \left (-\frac {2^{\frac {3}{5}} 3^{\frac {2}{5}} \ln \left (1+\frac {2^{\frac {1}{5}} 3^{\frac {4}{5}} \left (x^{5}\right )^{\frac {1}{5}}}{3}\right )}{2 \left (x^{5}\right )^{\frac {2}{5}}}-\frac {2^{\frac {3}{5}} 3^{\frac {2}{5}} \cos \left (\frac {2 \pi }{5}\right ) \ln \left (1-\frac {2 \cos \left (\frac {\pi }{5}\right ) 2^{\frac {1}{5}} 3^{\frac {4}{5}} \left (x^{5}\right )^{\frac {1}{5}}}{3}+\frac {2^{\frac {2}{5}} 3^{\frac {3}{5}} \left (x^{5}\right )^{\frac {2}{5}}}{3}\right )}{2 \left (x^{5}\right )^{\frac {2}{5}}}+\frac {72^{\frac {1}{5}} \arctan \left (\frac {\sin \left (\frac {\pi }{5}\right ) 2^{\frac {1}{5}} 3^{\frac {4}{5}} \left (x^{5}\right )^{\frac {1}{5}}}{3-\cos \left (\frac {\pi }{5}\right ) 2^{\frac {1}{5}} 3^{\frac {4}{5}} \left (x^{5}\right )^{\frac {1}{5}}}\right ) \sin \left (\frac {2 \pi }{5}\right )}{\left (x^{5}\right )^{\frac {2}{5}}}+\frac {2^{\frac {3}{5}} 3^{\frac {2}{5}} \cos \left (\frac {\pi }{5}\right ) \ln \left (1+\frac {2 \cos \left (\frac {2 \pi }{5}\right ) 2^{\frac {1}{5}} 3^{\frac {4}{5}} \left (x^{5}\right )^{\frac {1}{5}}}{3}+\frac {2^{\frac {2}{5}} 3^{\frac {3}{5}} \left (x^{5}\right )^{\frac {2}{5}}}{3}\right )}{2 \left (x^{5}\right )^{\frac {2}{5}}}-\frac {72^{\frac {1}{5}} \arctan \left (\frac {\sin \left (\frac {2 \pi }{5}\right ) 2^{\frac {1}{5}} 3^{\frac {4}{5}} \left (x^{5}\right )^{\frac {1}{5}}}{3+\cos \left (\frac {2 \pi }{5}\right ) 2^{\frac {1}{5}} 3^{\frac {4}{5}} \left (x^{5}\right )^{\frac {1}{5}}}\right ) \sin \left (\frac {\pi }{5}\right )}{\left (x^{5}\right )^{\frac {2}{5}}}\right )}{25}\right )}{6480}\) | \(277\) |
default | \(\frac {\frac {1}{75} x^{7}-\frac {3}{100} x^{2}}{\left (2 x^{5}+3\right )^{2}}+\frac {48^{\frac {2}{5}} \ln \left (x \sqrt {5}\, 48^{\frac {1}{5}}-x 48^{\frac {1}{5}}+48^{\frac {2}{5}}+4 x^{2}\right ) \sqrt {5}}{12000}+\frac {48^{\frac {2}{5}} \ln \left (x \sqrt {5}\, 48^{\frac {1}{5}}-x 48^{\frac {1}{5}}+48^{\frac {2}{5}}+4 x^{2}\right )}{12000}-\frac {48^{\frac {3}{5}} \sqrt {5}\, \arctan \left (\frac {\sqrt {5}\, 48^{\frac {1}{5}}}{\sqrt {10 \,48^{\frac {2}{5}}+2 \sqrt {5}\, 48^{\frac {2}{5}}}}-\frac {48^{\frac {1}{5}}}{\sqrt {10 \,48^{\frac {2}{5}}+2 \sqrt {5}\, 48^{\frac {2}{5}}}}+\frac {8 x}{\sqrt {10 \,48^{\frac {2}{5}}+2 \sqrt {5}\, 48^{\frac {2}{5}}}}\right )}{1500 \sqrt {10 \,48^{\frac {2}{5}}+2 \sqrt {5}\, 48^{\frac {2}{5}}}}+\frac {48^{\frac {2}{5}} \ln \left (-x \sqrt {5}\, 48^{\frac {1}{5}}+48^{\frac {2}{5}}-x 48^{\frac {1}{5}}+4 x^{2}\right )}{12000}-\frac {48^{\frac {2}{5}} \ln \left (-x \sqrt {5}\, 48^{\frac {1}{5}}+48^{\frac {2}{5}}-x 48^{\frac {1}{5}}+4 x^{2}\right ) \sqrt {5}}{12000}+\frac {48^{\frac {3}{5}} \arctan \left (-\frac {\sqrt {5}\, 48^{\frac {1}{5}}}{\sqrt {10 \,48^{\frac {2}{5}}-2 \sqrt {5}\, 48^{\frac {2}{5}}}}-\frac {48^{\frac {1}{5}}}{\sqrt {10 \,48^{\frac {2}{5}}-2 \sqrt {5}\, 48^{\frac {2}{5}}}}+\frac {8 x}{\sqrt {10 \,48^{\frac {2}{5}}-2 \sqrt {5}\, 48^{\frac {2}{5}}}}\right ) \sqrt {5}}{1500 \sqrt {10 \,48^{\frac {2}{5}}-2 \sqrt {5}\, 48^{\frac {2}{5}}}}+\frac {48^{\frac {2}{5}} \ln \left (48^{\frac {1}{5}}+2 x \right )}{150 \left (5+\sqrt {5}\right ) \left (\sqrt {5}-5\right )}\) | \(354\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.35, size = 335, normalized size = 1.05 \begin {gather*} \frac {3^{\frac {4}{5}} 2^{\frac {4}{5}} {\left (\sqrt {5} - 5\right )} \arctan \left (\frac {3^{\frac {4}{5}} 2^{\frac {4}{5}} {\left (4 \cdot 2^{\frac {2}{5}} x + \sqrt {5} 3^{\frac {1}{5}} 2^{\frac {1}{5}} - 3^{\frac {1}{5}} 2^{\frac {1}{5}}\right )}}{6 \, \sqrt {2 \, \sqrt {5} + 10}}\right )}{750 \, {\left (\sqrt {5} 3^{\frac {2}{5}} 2^{\frac {1}{5}} - 3^{\frac {2}{5}} 2^{\frac {1}{5}}\right )} \sqrt {2 \, \sqrt {5} + 10}} + \frac {3^{\frac {4}{5}} 2^{\frac {4}{5}} {\left (\sqrt {5} + 5\right )} \arctan \left (\frac {3^{\frac {4}{5}} 2^{\frac {4}{5}} {\left (4 \cdot 2^{\frac {2}{5}} x - \sqrt {5} 3^{\frac {1}{5}} 2^{\frac {1}{5}} - 3^{\frac {1}{5}} 2^{\frac {1}{5}}\right )}}{6 \, \sqrt {-2 \, \sqrt {5} + 10}}\right )}{750 \, {\left (\sqrt {5} 3^{\frac {2}{5}} 2^{\frac {1}{5}} + 3^{\frac {2}{5}} 2^{\frac {1}{5}}\right )} \sqrt {-2 \, \sqrt {5} + 10}} - \frac {1}{1500} \cdot 3^{\frac {2}{5}} 2^{\frac {3}{5}} \log \left (2^{\frac {1}{5}} x + 3^{\frac {1}{5}}\right ) + \frac {4 \, x^{7} - 9 \, x^{2}}{300 \, {\left (4 \, x^{10} + 12 \, x^{5} + 9\right )}} - \frac {\log \left (2 \cdot 2^{\frac {2}{5}} x^{2} - x {\left (\sqrt {5} 3^{\frac {1}{5}} 2^{\frac {1}{5}} + 3^{\frac {1}{5}} 2^{\frac {1}{5}}\right )} + 2 \cdot 3^{\frac {2}{5}}\right )}{250 \, {\left (\sqrt {5} 3^{\frac {3}{5}} 2^{\frac {2}{5}} + 3^{\frac {3}{5}} 2^{\frac {2}{5}}\right )}} + \frac {\log \left (2 \cdot 2^{\frac {2}{5}} x^{2} + x {\left (\sqrt {5} 3^{\frac {1}{5}} 2^{\frac {1}{5}} - 3^{\frac {1}{5}} 2^{\frac {1}{5}}\right )} + 2 \cdot 3^{\frac {2}{5}}\right )}{250 \, {\left (\sqrt {5} 3^{\frac {3}{5}} 2^{\frac {2}{5}} - 3^{\frac {3}{5}} 2^{\frac {2}{5}}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [C] Result contains complex when optimal does not.
time = 3.22, size = 1751, normalized size = 5.49
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.14, size = 37, normalized size = 0.12 \begin {gather*} \frac {4 x^{7} - 9 x^{2}}{1200 x^{10} + 3600 x^{5} + 2700} + \operatorname {RootSum} {\left (105468750000000 t^{5} + 1, \left ( t \mapsto t \log {\left (- 281250000 t^{3} + x \right )} \right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.15, size = 481, normalized size = 1.51 \begin {gather*} \frac {1}{12000} \left (\left (\left (\frac {3}{2}\right )^{\frac {1}{5}}\right )^{2} \left (2 \sqrt {5}+10\right )-5 \left (\left (\frac {3}{2}\right )^{\frac {1}{5}}\right )^{2}+2 \left (\left (\frac {3}{2}\right )^{\frac {1}{5}}\right )^{2} \sqrt {5}-\left (\left (\frac {3}{2}\right )^{\frac {1}{5}}\right )^{2}\right ) \ln \left (x^{2}+\frac {1}{2} \left (\left (\frac {3}{2}\right )^{\frac {1}{5}} \sqrt {5}-\left (\frac {3}{2}\right )^{\frac {1}{5}}\right ) x+\left (\frac {3}{2}\right )^{\frac {1}{5}} \left (\frac {3}{2}\right )^{\frac {1}{5}}\right )+\frac {1}{3000} \left (\left (\left (\frac {3}{2}\right )^{\frac {1}{5}}\right )^{2} \sqrt {2 \sqrt {5}+10} \sqrt {5}-\left (\left (\frac {3}{2}\right )^{\frac {1}{5}}\right )^{2} \sqrt {2 \sqrt {5}+10}\right ) \arctan \left (-\frac {x+\frac {1}{4} \left (\sqrt {5}-1\right ) \left (\frac {3}{2}\right )^{\frac {1}{5}}}{\frac {1}{4} \sqrt {2 \sqrt {5}+10} \left (\frac {3}{2}\right )^{\frac {1}{5}}}\right )-\frac {1}{750} \left (\frac {3}{2}\right )^{\frac {1}{5}} \left (\frac {3}{2}\right )^{\frac {1}{5}} \ln \left |x+\left (\frac {3}{2}\right )^{\frac {1}{5}}\right |+\frac {1}{12000} \left (\left (\left (\frac {3}{2}\right )^{\frac {1}{5}}\right )^{2} \left (-2 \sqrt {5}+10\right )-5 \left (\left (\frac {3}{2}\right )^{\frac {1}{5}}\right )^{2}-2 \left (\left (\frac {3}{2}\right )^{\frac {1}{5}}\right )^{2} \sqrt {5}-\left (\left (\frac {3}{2}\right )^{\frac {1}{5}}\right )^{2}\right ) \ln \left (x^{2}+\frac {1}{2} \left (-\left (\frac {3}{2}\right )^{\frac {1}{5}} \sqrt {5}-\left (\frac {3}{2}\right )^{\frac {1}{5}}\right ) x+\left (\frac {3}{2}\right )^{\frac {1}{5}} \left (\frac {3}{2}\right )^{\frac {1}{5}}\right )+\frac {1}{3000} \left (-\left (\left (\frac {3}{2}\right )^{\frac {1}{5}}\right )^{2} \sqrt {-2 \sqrt {5}+10} \sqrt {5}-\left (\left (\frac {3}{2}\right )^{\frac {1}{5}}\right )^{2} \sqrt {-2 \sqrt {5}+10}\right ) \arctan \left (-\frac {x-\frac {1}{4} \left (\sqrt {5}+1\right ) \left (\frac {3}{2}\right )^{\frac {1}{5}}}{\frac {1}{4} \sqrt {-2 \sqrt {5}+10} \left (\frac {3}{2}\right )^{\frac {1}{5}}}\right )+\frac {4 x^{7}-9 x^{2}}{300 \left (2 x^{5}+3\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.60, size = 285, normalized size = 0.89 \begin {gather*} \frac {3^{2/5}\,\ln \left (x-\frac {3^{1/5}\,{\left (2\,2^{1/10}\,\sqrt {-\sqrt {5}-5}-2^{3/5}\,\left (\sqrt {5}-1\right )\right )}^3}{256}\right )\,\left (2\,2^{1/10}\,\sqrt {-\sqrt {5}-5}-2^{3/5}\,\left (\sqrt {5}-1\right )\right )}{6000}-\frac {\frac {3\,x^2}{400}-\frac {x^7}{300}}{x^{10}+3\,x^5+\frac {9}{4}}-\frac {3^{2/5}\,\ln \left (x+\frac {3^{1/5}\,{\left (2\,2^{1/10}\,\sqrt {-\sqrt {5}-5}+2^{3/5}\,\left (\sqrt {5}-1\right )\right )}^3}{256}\right )\,\left (2\,2^{1/10}\,\sqrt {-\sqrt {5}-5}+2^{3/5}\,\left (\sqrt {5}-1\right )\right )}{6000}-\frac {{72}^{1/5}\,\ln \left (x+\frac {{72}^{3/5}}{12}\right )}{1500}+\frac {3^{2/5}\,\ln \left (x-\frac {3^{1/5}\,{\left (2^{3/5}\,\left (\sqrt {5}+1\right )-2\,2^{1/10}\,\sqrt {\sqrt {5}-5}\right )}^3}{256}\right )\,\left (2^{3/5}\,\left (\sqrt {5}+1\right )-2\,2^{1/10}\,\sqrt {\sqrt {5}-5}\right )}{6000}+\frac {3^{2/5}\,\ln \left (x-\frac {3^{1/5}\,{\left (2^{3/5}\,\left (\sqrt {5}+1\right )+2\,2^{1/10}\,\sqrt {\sqrt {5}-5}\right )}^3}{256}\right )\,\left (2^{3/5}\,\left (\sqrt {5}+1\right )+2\,2^{1/10}\,\sqrt {\sqrt {5}-5}\right )}{6000} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________