Optimal. Leaf size=69 \[ \frac {b e m n \text {Int}\left (\frac {x^{m-1}}{\left (d+e x^m\right ) \log ^2\left (f x^p\right )},x\right )}{2 p}-\frac {a+b \log \left (c \left (d+e x^m\right )^n\right )}{2 p \log ^2\left (f x^p\right )} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.12, 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 = {} \[ \int \frac {a+b \log \left (c \left (d+e x^m\right )^n\right )}{x \log ^3\left (f x^p\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {a+b \log \left (c \left (d+e x^m\right )^n\right )}{x \log ^3\left (f x^p\right )} \, dx &=-\frac {a+b \log \left (c \left (d+e x^m\right )^n\right )}{2 p \log ^2\left (f x^p\right )}+\frac {(b e m n) \int \frac {x^{-1+m}}{\left (d+e x^m\right ) \log ^2\left (f x^p\right )} \, dx}{2 p}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 11.06, size = 0, normalized size = 0.00 \[ \int \frac {a+b \log \left (c \left (d+e x^m\right )^n\right )}{x \log ^3\left (f x^p\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.26, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {b \log \left ({\left (e x^{m} + d\right )}^{n} c\right ) + a}{x \log \left (f x^{p}\right )^{3}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {b \log \left ({\left (e x^{m} + d\right )}^{n} c\right ) + a}{x \log \left (f x^{p}\right )^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.22, size = 0, normalized size = 0.00 \[ \int \frac {b \ln \left (c \left (e \,x^{m}+d \right )^{n}\right )+a}{x \ln \left (f \,x^{p}\right )^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {1}{2} \, {\left (2 \, d e m^{2} n \int \frac {x^{m}}{2 \, {\left (e^{2} p^{2} x x^{2 \, m} \log \relax (f) + 2 \, d e p^{2} x x^{m} \log \relax (f) + d^{2} p^{2} x \log \relax (f) + {\left (e^{2} p^{2} x x^{2 \, m} + 2 \, d e p^{2} x x^{m} + d^{2} p^{2} x\right )} \log \left (x^{p}\right )\right )}}\,{d x} - \frac {e m n x^{m} \log \left (x^{p}\right ) + d p \log \relax (c) + {\left (e m n \log \relax (f) + e p \log \relax (c)\right )} x^{m} + {\left (e p x^{m} + d p\right )} \log \left ({\left (e x^{m} + d\right )}^{n}\right )}{e p^{2} x^{m} \log \relax (f)^{2} + d p^{2} \log \relax (f)^{2} + {\left (e p^{2} x^{m} + d p^{2}\right )} \log \left (x^{p}\right )^{2} + 2 \, {\left (e p^{2} x^{m} \log \relax (f) + d p^{2} \log \relax (f)\right )} \log \left (x^{p}\right )}\right )} b - \frac {a}{2 \, p \log \left (f x^{p}\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.01 \[ \int \frac {a+b\,\ln \left (c\,{\left (d+e\,x^m\right )}^n\right )}{x\,{\ln \left (f\,x^p\right )}^3} \,d x \]
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]
________________________________________________________________________________________