Optimal. Leaf size=24 \[ \frac{x^{2 n}}{2 a n \left (a+b x^n\right )^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0051769, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {264} \[ \frac{x^{2 n}}{2 a n \left (a+b x^n\right )^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 264
Rubi steps
\begin{align*} \int \frac{x^{-1+2 n}}{\left (a+b x^n\right )^3} \, dx &=\frac{x^{2 n}}{2 a n \left (a+b x^n\right )^2}\\ \end{align*}
Mathematica [A] time = 0.0058874, size = 24, normalized size = 1. \[ \frac{x^{2 n}}{2 a n \left (a+b x^n\right )^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.025, size = 36, normalized size = 1.5 \begin{align*}{\frac{1}{ \left ( a+b{{\rm e}^{n\ln \left ( x \right ) }} \right ) ^{2}} \left ( -{\frac{{{\rm e}^{n\ln \left ( x \right ) }}}{bn}}-{\frac{a}{2\,{b}^{2}n}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.967291, size = 55, normalized size = 2.29 \begin{align*} -\frac{2 \, b x^{n} + a}{2 \,{\left (b^{4} n x^{2 \, n} + 2 \, a b^{3} n x^{n} + a^{2} b^{2} n\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.00395, size = 86, normalized size = 3.58 \begin{align*} -\frac{2 \, b x^{n} + a}{2 \,{\left (b^{4} n x^{2 \, n} + 2 \, a b^{3} n x^{n} + a^{2} b^{2} n\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{2 \, n - 1}}{{\left (b x^{n} + a\right )}^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]