Optimal. Leaf size=39 \[ -\frac{f^a \left (-b \log (f) x^n\right )^{3/n} \text{Gamma}\left (-\frac{3}{n},-b \log (f) x^n\right )}{n x^3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0241303, antiderivative size = 39, 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} \[ -\frac{f^a \left (-b \log (f) x^n\right )^{3/n} \text{Gamma}\left (-\frac{3}{n},-b \log (f) x^n\right )}{n x^3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2218
Rubi steps
\begin{align*} \int \frac{f^{a+b x^n}}{x^4} \, dx &=-\frac{f^a \Gamma \left (-\frac{3}{n},-b x^n \log (f)\right ) \left (-b x^n \log (f)\right )^{3/n}}{n x^3}\\ \end{align*}
Mathematica [A] time = 0.0041876, size = 39, normalized size = 1. \[ -\frac{f^a \left (-b \log (f) x^n\right )^{3/n} \text{Gamma}\left (-\frac{3}{n},-b \log (f) x^n\right )}{n x^3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F] time = 0.023, size = 0, normalized size = 0. \begin{align*} \int{\frac{{f}^{a+b{x}^{n}}}{{x}^{4}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.19786, size = 53, normalized size = 1.36 \begin{align*} -\frac{\left (-b x^{n} \log \left (f\right )\right )^{\frac{3}{n}} f^{a} \Gamma \left (-\frac{3}{n}, -b x^{n} \log \left (f\right )\right )}{n x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{f^{b x^{n} + a}}{x^{4}}, x\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{f^{b x^{n} + a}}{x^{4}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]