Optimal. Leaf size=39 \[ \frac{3}{20 \left (2 x^5+3\right )}-\frac{9}{80 \left (2 x^5+3\right )^2}+\frac{1}{40} \log \left (2 x^5+3\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0249247, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac{3}{20 \left (2 x^5+3\right )}-\frac{9}{80 \left (2 x^5+3\right )^2}+\frac{1}{40} \log \left (2 x^5+3\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^{14}}{\left (3+2 x^5\right )^3} \, dx &=\frac{1}{5} \operatorname{Subst}\left (\int \frac{x^2}{(3+2 x)^3} \, dx,x,x^5\right )\\ &=\frac{1}{5} \operatorname{Subst}\left (\int \left (\frac{9}{4 (3+2 x)^3}-\frac{3}{2 (3+2 x)^2}+\frac{1}{4 (3+2 x)}\right ) \, dx,x,x^5\right )\\ &=-\frac{9}{80 \left (3+2 x^5\right )^2}+\frac{3}{20 \left (3+2 x^5\right )}+\frac{1}{40} \log \left (3+2 x^5\right )\\ \end{align*}
Mathematica [A] time = 0.0134275, size = 33, normalized size = 0.85 \[ \frac{1}{80} \left (\frac{3 \left (8 x^5+9\right )}{\left (2 x^5+3\right )^2}+2 \log \left (2 x^5+3\right )\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.009, size = 34, normalized size = 0.9 \begin{align*} -{\frac{9}{80\, \left ( 2\,{x}^{5}+3 \right ) ^{2}}}+{\frac{3}{40\,{x}^{5}+60}}+{\frac{\ln \left ( 2\,{x}^{5}+3 \right ) }{40}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.923762, size = 46, normalized size = 1.18 \begin{align*} \frac{3 \,{\left (8 \, x^{5} + 9\right )}}{80 \,{\left (4 \, x^{10} + 12 \, x^{5} + 9\right )}} + \frac{1}{40} \, \log \left (2 \, x^{5} + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.9503, size = 112, normalized size = 2.87 \begin{align*} \frac{24 \, x^{5} + 2 \,{\left (4 \, x^{10} + 12 \, x^{5} + 9\right )} \log \left (2 \, x^{5} + 3\right ) + 27}{80 \,{\left (4 \, x^{10} + 12 \, x^{5} + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.171112, size = 27, normalized size = 0.69 \begin{align*} \frac{24 x^{5} + 27}{320 x^{10} + 960 x^{5} + 720} + \frac{\log{\left (2 x^{5} + 3 \right )}}{40} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.10811, size = 41, normalized size = 1.05 \begin{align*} -\frac{3 \,{\left (x^{10} + x^{5}\right )}}{20 \,{\left (2 \, x^{5} + 3\right )}^{2}} + \frac{1}{40} \, \log \left ({\left | 2 \, x^{5} + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]