Optimal. Leaf size=76 \[ \frac {\left (a x^m+b \log ^q\left (c x^n\right )\right )^{p+1}}{b n (p+1) q}-\frac {a m \text {Int}\left (x^{m-1} \left (a x^m+b \log ^q\left (c x^n\right )\right )^p,x\right )}{b n q} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.25, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\log ^{-1+q}\left (c x^n\right ) \left (a x^m+b \log ^q\left (c x^n\right )\right )^p}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\log ^{-1+q}\left (c x^n\right ) \left (a x^m+b \log ^q\left (c x^n\right )\right )^p}{x} \, dx &=\frac {\left (a x^m+b \log ^q\left (c x^n\right )\right )^{1+p}}{b n (1+p) q}-\frac {(a m) \int x^{-1+m} \left (a x^m+b \log ^q\left (c x^n\right )\right )^p \, dx}{b n q}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 1.26, size = 0, normalized size = 0.00 \[ \int \frac {\log ^{-1+q}\left (c x^n\right ) \left (a x^m+b \log ^q\left (c x^n\right )\right )^p}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.49, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (a x^{m} + b \log \left (c x^{n}\right )^{q}\right )}^{p} \log \left (c x^{n}\right )^{q - 1}}{x}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.85, size = 0, normalized size = 0.00 \[ \int \frac {\left (a \,x^{m}+b \ln \left (c \,x^{n}\right )^{q}\right )^{p} \ln \left (c \,x^{n}\right )^{q -1}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.01 \[ \int \frac {{\ln \left (c\,x^n\right )}^{q-1}\,{\left (a\,x^m+b\,{\ln \left (c\,x^n\right )}^q\right )}^p}{x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________