Optimal. Leaf size=27 \[ \text {Int}\left (\frac {\left (a+b \log \left (c \left (d+e \sqrt {x}\right )^2\right )\right )^p}{x},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.05, 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 = {} \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt {x}\right )^2\right )\right )^p}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\left (a+b \log \left (c \left (d+e \sqrt {x}\right )^2\right )\right )^p}{x} \, dx &=2 \operatorname {Subst}\left (\int \frac {\left (a+b \log \left (c (d+e x)^2\right )\right )^p}{x} \, dx,x,\sqrt {x}\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.12, size = 0, normalized size = 0.00 \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt {x}\right )^2\right )\right )^p}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.48, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (b \log \left (c e^{2} x + 2 \, c d e \sqrt {x} + c d^{2}\right ) + a\right )}^{p}}{x}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b \log \left ({\left (e \sqrt {x} + d\right )}^{2} c\right ) + a\right )}^{p}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.07, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \ln \left (\left (e \sqrt {x}+d \right )^{2} c \right )+a \right )^{p}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b \log \left ({\left (e \sqrt {x} + d\right )}^{2} c\right ) + a\right )}^{p}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {{\left (a+b\,\ln \left (c\,{\left (d+e\,\sqrt {x}\right )}^2\right )\right )}^p}{x} \,d x \]
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]
________________________________________________________________________________________