Optimal. Leaf size=31 \[ \text {Int}\left (\frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.09, 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 = {} \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^2} \, dx &=\int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^2} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 2.63, size = 0, normalized size = 0.00 \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{(g+h x)^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.42, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {F^{b f \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + a f}}{h^{2} x^{2} + 2 \, g h x + g^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + a\right )} f}}{{\left (h x + g\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.60, size = 0, normalized size = 0.00 \[ \int \frac {F^{\left (b \ln \left (c \left (e x +d \right )^{n}\right )^{2}+a \right ) f}}{\left (h x +g \right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + a\right )} f}}{{\left (h x + g\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {{\mathrm {e}}^{f\,\ln \relax (F)\,\left (b\,{\ln \left (c\,{\left (d+e\,x\right )}^n\right )}^2+a\right )}}{{\left (g+h\,x\right )}^2} \,d x \]
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]
________________________________________________________________________________________