Optimal. Leaf size=22 \[ x \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}} \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {1971, 29}
\begin {gather*} x \log (x) \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 29
Rule 1971
Rubi steps
\begin {align*} \int \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}} \, dx &=\left (x \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}}\right ) \int \frac {1}{x} \, dx\\ &=x \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}} \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 22, normalized size = 1.00 \begin {gather*} x \left (a \left (b x^m\right )^n\right )^{-\frac {1}{m n}} \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F]
time = 0.04, size = 0, normalized size = 0.00 \[\int \left (a \left (b \,x^{m}\right )^{n}\right )^{-\frac {1}{m n}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 19, normalized size = 0.86 \begin {gather*} e^{\left (-\frac {n \log \left (b\right ) + \log \left (a\right )}{m n}\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a \left (b x^{m}\right )^{n}\right )^{- \frac {1}{m n}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 2.16, size = 19, normalized size = 0.86 \begin {gather*} e^{\left (-\frac {n \log \left (b\right ) + \log \left (a\right )}{m n}\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [F]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {1}{{\left (a\,{\left (b\,x^m\right )}^n\right )}^{\frac {1}{m\,n}}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________