Optimal. Leaf size=33 \[ -\frac{1}{3 a^3 x^3}+\frac{\log \left (a^3+x^3\right )}{3 a^6}-\frac{\log (x)}{a^6} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0195942, antiderivative size = 33, 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, 44} \[ -\frac{1}{3 a^3 x^3}+\frac{\log \left (a^3+x^3\right )}{3 a^6}-\frac{\log (x)}{a^6} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 44
Rubi steps
\begin{align*} \int \frac{1}{x^4 \left (a^3+x^3\right )} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{1}{x^2 \left (a^3+x\right )} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (\frac{1}{a^3 x^2}-\frac{1}{a^6 x}+\frac{1}{a^6 \left (a^3+x\right )}\right ) \, dx,x,x^3\right )\\ &=-\frac{1}{3 a^3 x^3}-\frac{\log (x)}{a^6}+\frac{\log \left (a^3+x^3\right )}{3 a^6}\\ \end{align*}
Mathematica [A] time = 0.0052609, size = 33, normalized size = 1. \[ -\frac{1}{3 a^3 x^3}+\frac{\log \left (a^3+x^3\right )}{3 a^6}-\frac{\log (x)}{a^6} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 43, normalized size = 1.3 \begin{align*} -{\frac{1}{3\,{a}^{3}{x}^{3}}}-{\frac{\ln \left ( x \right ) }{{a}^{6}}}+{\frac{\ln \left ({a}^{2}-ax+{x}^{2} \right ) }{3\,{a}^{6}}}+{\frac{\ln \left ( a+x \right ) }{3\,{a}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.925473, size = 42, normalized size = 1.27 \begin{align*} \frac{\log \left (a^{3} + x^{3}\right )}{3 \, a^{6}} - \frac{\log \left (x^{3}\right )}{3 \, a^{6}} - \frac{1}{3 \, a^{3} x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.037, size = 77, normalized size = 2.33 \begin{align*} \frac{x^{3} \log \left (a^{3} + x^{3}\right ) - 3 \, x^{3} \log \left (x\right ) - a^{3}}{3 \, a^{6} x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.391197, size = 29, normalized size = 0.88 \begin{align*} - \frac{1}{3 a^{3} x^{3}} - \frac{\log{\left (x \right )}}{a^{6}} + \frac{\log{\left (a^{3} + x^{3} \right )}}{3 a^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.05288, size = 54, normalized size = 1.64 \begin{align*} \frac{\log \left ({\left | a^{3} + x^{3} \right |}\right )}{3 \, a^{6}} - \frac{\log \left ({\left | x \right |}\right )}{a^{6}} - \frac{a^{3} - x^{3}}{3 \, a^{6} x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]