Optimal. Leaf size=123 \[ \frac {g^2 \text {Int}\left (\frac {1}{(f+g x) \left (a+b \log \left (c (d+e x)^n\right )\right )},x\right )}{(g h-f i)^2}-\frac {g i \text {Int}\left (\frac {1}{(h+i x) \left (a+b \log \left (c (d+e x)^n\right )\right )},x\right )}{(g h-f i)^2}-\frac {i \text {Int}\left (\frac {1}{(h+i x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )},x\right )}{g h-f i} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.23, 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 = {} \[ \int \frac {1}{(f+g x) (h+i x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {1}{(h+237 x)^2 (f+g x) \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx &=\int \left (\frac {237}{(237 f-g h) (h+237 x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}-\frac {237 g}{(237 f-g h)^2 (h+237 x) \left (a+b \log \left (c (d+e x)^n\right )\right )}+\frac {g^2}{(237 f-g h)^2 (f+g x) \left (a+b \log \left (c (d+e x)^n\right )\right )}\right ) \, dx\\ &=-\frac {(237 g) \int \frac {1}{(h+237 x) \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx}{(237 f-g h)^2}+\frac {g^2 \int \frac {1}{(f+g x) \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx}{(237 f-g h)^2}+\frac {237 \int \frac {1}{(h+237 x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx}{237 f-g h}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 3.28, size = 0, normalized size = 0.00 \[ \int \frac {1}{(f+g x) (h+i x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{a g i^{2} x^{3} + a f h^{2} + {\left (2 \, a g h i + a f i^{2}\right )} x^{2} + {\left (a g h^{2} + 2 \, a f h i\right )} x + {\left (b g i^{2} x^{3} + b f h^{2} + {\left (2 \, b g h i + b f i^{2}\right )} x^{2} + {\left (b g h^{2} + 2 \, b f h i\right )} x\right )} \log \left ({\left (e x + d\right )}^{n} c\right )}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (g x + f\right )} {\left (i x + h\right )}^{2} {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 1.58, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (g x +f \right ) \left (i x +h \right )^{2} \left (b \ln \left (c \left (e x +d \right )^{n}\right )+a \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (g x + f\right )} {\left (i x + h\right )}^{2} {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.01 \[ \int \frac {1}{\left (f+g\,x\right )\,{\left (h+i\,x\right )}^2\,\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (a + b \log {\left (c \left (d + e x\right )^{n} \right )}\right ) \left (f + g x\right ) \left (h + i x\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________