Optimal. Leaf size=34 \[ -\frac{f^a \sqrt [3]{-b x^3 \log (f)} \text{Gamma}\left (-\frac{1}{3},-b x^3 \log (f)\right )}{3 x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0216656, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {2218} \[ -\frac{f^a \sqrt [3]{-b x^3 \log (f)} \text{Gamma}\left (-\frac{1}{3},-b x^3 \log (f)\right )}{3 x} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2218
Rubi steps
\begin{align*} \int \frac{f^{a+b x^3}}{x^2} \, dx &=-\frac{f^a \Gamma \left (-\frac{1}{3},-b x^3 \log (f)\right ) \sqrt [3]{-b x^3 \log (f)}}{3 x}\\ \end{align*}
Mathematica [A] time = 0.0037348, size = 34, normalized size = 1. \[ -\frac{f^a \sqrt [3]{-b x^3 \log (f)} \text{Gamma}\left (-\frac{1}{3},-b x^3 \log (f)\right )}{3 x} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] time = 0.022, size = 100, normalized size = 2.9 \begin{align*}{\frac{{f}^{a}}{3}\sqrt [3]{-b}\sqrt [3]{\ln \left ( f \right ) } \left ( 3\,{\frac{{x}^{2} \left ( \ln \left ( f \right ) \right ) ^{2/3}b\Gamma \left ( 2/3 \right ) }{\sqrt [3]{-b} \left ( -b{x}^{3}\ln \left ( f \right ) \right ) ^{2/3}}}-3\,{\frac{{{\rm e}^{b{x}^{3}\ln \left ( f \right ) }}}{x\sqrt [3]{-b}\sqrt [3]{\ln \left ( f \right ) }}}-3\,{\frac{{x}^{2} \left ( \ln \left ( f \right ) \right ) ^{2/3}b\Gamma \left ( 2/3,-b{x}^{3}\ln \left ( f \right ) \right ) }{\sqrt [3]{-b} \left ( -b{x}^{3}\ln \left ( f \right ) \right ) ^{2/3}}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.23225, size = 38, normalized size = 1.12 \begin{align*} -\frac{\left (-b x^{3} \log \left (f\right )\right )^{\frac{1}{3}} f^{a} \Gamma \left (-\frac{1}{3}, -b x^{3} \log \left (f\right )\right )}{3 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.81136, size = 96, normalized size = 2.82 \begin{align*} \frac{\left (-b \log \left (f\right )\right )^{\frac{1}{3}} f^{a} x \Gamma \left (\frac{2}{3}, -b x^{3} \log \left (f\right )\right ) - f^{b x^{3} + a}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{f^{a + b x^{3}}}{x^{2}}\, dx \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{f^{b x^{3} + a}}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]