Optimal. Leaf size=26 \[ \text {Int}\left (\left (a+b \log \left (c x^n\right )\right ) \log \left (d \left (e+f x^m\right )^k\right ),x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, 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 = {}
\begin {gather*} \int \left (a+b \log \left (c x^n\right )\right ) \log \left (d \left (e+f x^m\right )^k\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \left (a+b \log \left (c x^n\right )\right ) \log \left (d \left (e+f x^m\right )^k\right ) \, dx &=\int \left (a+b \log \left (c x^n\right )\right ) \log \left (d \left (e+f x^m\right )^k\right ) \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] Leaf count is larger than twice the leaf count of optimal. \(165\) vs. \(2(26)=52\).
time = 0.12, size = 165, normalized size = 6.35 \begin {gather*} b k m n x-k m x \left (a+b \left (-n \log (x)+\log \left (c x^n\right )\right )\right )+x \left (b k m n-b k m n \, _3F_2\left (1,\frac {1}{m},\frac {1}{m};1+\frac {1}{m},1+\frac {1}{m};-\frac {f x^m}{e}\right )-b k m n \log (x)+k m \, _2F_1\left (1,\frac {1}{m};1+\frac {1}{m};-\frac {f x^m}{e}\right ) \left (a-b n+b \log \left (c x^n\right )\right )+a \log \left (d \left (e+f x^m\right )^k\right )-b n \log \left (d \left (e+f x^m\right )^k\right )+b \log \left (c x^n\right ) \log \left (d \left (e+f x^m\right )^k\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 0, normalized size = 0.00 \[\int \left (a +b \ln \left (c \,x^{n}\right )\right ) \ln \left (d \left (e +f \,x^{m}\right )^{k}\right )\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a + b \log {\left (c x^{n} \right )}\right ) \log {\left (d \left (e + f x^{m}\right )^{k} \right )}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \ln \left (d\,{\left (e+f\,x^m\right )}^k\right )\,\left (a+b\,\ln \left (c\,x^n\right )\right ) \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________