Optimal. Leaf size=19 \[ \frac{x^{10}}{10 b \left (a x^5+b\right )^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.006112, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {1593, 264} \[ \frac{x^{10}}{10 b \left (a x^5+b\right )^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1593
Rule 264
Rubi steps
\begin{align*} \int \frac{1}{\left (\frac{b}{x^3}+a x^2\right )^3} \, dx &=\int \frac{x^9}{\left (b+a x^5\right )^3} \, dx\\ &=\frac{x^{10}}{10 b \left (b+a x^5\right )^2}\\ \end{align*}
Mathematica [A] time = 0.0087693, size = 24, normalized size = 1.26 \[ -\frac{2 a x^5+b}{10 a^2 \left (a x^5+b\right )^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 31, normalized size = 1.6 \begin{align*}{\frac{b}{10\,{a}^{2} \left ( a{x}^{5}+b \right ) ^{2}}}-{\frac{1}{5\,{a}^{2} \left ( a{x}^{5}+b \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] time = 1.0571, size = 49, normalized size = 2.58 \begin{align*} -\frac{2 \, a x^{5} + b}{10 \,{\left (a^{4} x^{10} + 2 \, a^{3} b x^{5} + a^{2} b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 0.631051, size = 76, normalized size = 4. \begin{align*} -\frac{2 \, a x^{5} + b}{10 \,{\left (a^{4} x^{10} + 2 \, a^{3} b x^{5} + a^{2} b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 5.42171, size = 36, normalized size = 1.89 \begin{align*} - \frac{2 a x^{5} + b}{10 a^{4} x^{10} + 20 a^{3} b x^{5} + 10 a^{2} b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.1578, size = 30, normalized size = 1.58 \begin{align*} -\frac{2 \, a x^{5} + b}{10 \,{\left (a x^{5} + b\right )}^{2} a^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]