Optimal. Leaf size=32 \[ -\frac{x^{-3 (n+1)} \left (a x^2+b x^3\right )^{n+1}}{a (n+1)} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0251077, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, Rules used = {2014} \[ -\frac{x^{-3 (n+1)} \left (a x^2+b x^3\right )^{n+1}}{a (n+1)} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2014
Rubi steps
\begin{align*} \int x^{-2-3 n} \left (a x^2+b x^3\right )^n \, dx &=-\frac{x^{-3 (1+n)} \left (a x^2+b x^3\right )^{1+n}}{a (1+n)}\\ \end{align*}
Mathematica [A] time = 0.014193, size = 30, normalized size = 0.94 \[ -\frac{x^{-3 (n+1)} \left (x^2 (a+b x)\right )^{n+1}}{a (n+1)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 36, normalized size = 1.1 \begin{align*} -{\frac{{x}^{-1-3\,n} \left ( bx+a \right ) \left ( b{x}^{3}+a{x}^{2} \right ) ^{n}}{a \left ( 1+n \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (b x^{3} + a x^{2}\right )}^{n} x^{-3 \, n - 2}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0.946151, size = 77, normalized size = 2.41 \begin{align*} -\frac{{\left (b x^{2} + a x\right )}{\left (b x^{3} + a x^{2}\right )}^{n} x^{-3 \, n - 2}}{a n + a} \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{\left (b x^{3} + a x^{2}\right )}^{n} x^{-3 \, n - 2}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]