Optimal. Leaf size=20 \[ -\frac{\left (b x^n\right )^p}{x^2 (2-n p)} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0073232, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {15, 30} \[ -\frac{\left (b x^n\right )^p}{x^2 (2-n p)} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{\left (b x^n\right )^p}{x^3} \, dx &=\left (x^{-n p} \left (b x^n\right )^p\right ) \int x^{-3+n p} \, dx\\ &=-\frac{\left (b x^n\right )^p}{(2-n p) x^2}\\ \end{align*}
Mathematica [A] time = 0.0024106, size = 18, normalized size = 0.9 \[ \frac{\left (b x^n\right )^p}{x^2 (n p-2)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 19, normalized size = 1. \begin{align*}{\frac{ \left ( b{x}^{n} \right ) ^{p}}{{x}^{2} \left ( np-2 \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.983745, size = 26, normalized size = 1.3 \begin{align*} \frac{b^{p}{\left (x^{n}\right )}^{p}}{{\left (n p - 2\right )} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.34775, size = 58, normalized size = 2.9 \begin{align*} \frac{e^{\left (n p \log \left (x\right ) + p \log \left (b\right )\right )}}{{\left (n p - 2\right )} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \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{\left (b x^{n}\right )^{p}}{x^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]