\(\int \frac {\log (c (d+e x^n)^p)}{f+g x} \, dx\) [216]

Optimal result

Integrand size = 20, antiderivative size = 20 \[ \int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{f+g x} \, dx=\text {Int}\left (\frac {\log \left (c \left (d+e x^n\right )^p\right )}{f+g x},x\right ) \]

[Out]

Unintegrable(ln(c*(d+e*x^n)^p)/(g*x+f),x)

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{f+g x} \, dx=\int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{f+g x} \, dx \]

[In]

Int[Log[c*(d + e*x^n)^p]/(f + g*x),x]

[Out]

Defer[Int][Log[c*(d + e*x^n)^p]/(f + g*x), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{f+g x} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 1.54 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{f+g x} \, dx=\int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{f+g x} \, dx \]

[In]

Integrate[Log[c*(d + e*x^n)^p]/(f + g*x),x]

[Out]

Integrate[Log[c*(d + e*x^n)^p]/(f + g*x), x]

Maple [N/A]

Not integrable

Time = 0.19 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00

\[\int \frac {\ln \left (c \left (d +e \,x^{n}\right )^{p}\right )}{g x +f}d x\]

[In]

int(ln(c*(d+e*x^n)^p)/(g*x+f),x)

[Out]

int(ln(c*(d+e*x^n)^p)/(g*x+f),x)

Fricas [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{f+g x} \, dx=\int { \frac {\log \left ({\left (e x^{n} + d\right )}^{p} c\right )}{g x + f} \,d x } \]

[In]

integrate(log(c*(d+e*x^n)^p)/(g*x+f),x, algorithm="fricas")

[Out]

integral(log((e*x^n + d)^p*c)/(g*x + f), x)

Sympy [N/A]

Not integrable

Time = 3.05 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{f+g x} \, dx=\int \frac {\log {\left (c \left (d + e x^{n}\right )^{p} \right )}}{f + g x}\, dx \]

[In]

integrate(ln(c*(d+e*x**n)**p)/(g*x+f),x)

[Out]

Integral(log(c*(d + e*x**n)**p)/(f + g*x), x)

Maxima [N/A]

Not integrable

Time = 0.34 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{f+g x} \, dx=\int { \frac {\log \left ({\left (e x^{n} + d\right )}^{p} c\right )}{g x + f} \,d x } \]

[In]

integrate(log(c*(d+e*x^n)^p)/(g*x+f),x, algorithm="maxima")

[Out]

integrate(log((e*x^n + d)^p*c)/(g*x + f), x)

Giac [N/A]

Not integrable

Time = 0.34 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{f+g x} \, dx=\int { \frac {\log \left ({\left (e x^{n} + d\right )}^{p} c\right )}{g x + f} \,d x } \]

[In]

integrate(log(c*(d+e*x^n)^p)/(g*x+f),x, algorithm="giac")

[Out]

integrate(log((e*x^n + d)^p*c)/(g*x + f), x)

Mupad [N/A]

Not integrable

Time = 1.32 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{f+g x} \, dx=\int \frac {\ln \left (c\,{\left (d+e\,x^n\right )}^p\right )}{f+g\,x} \,d x \]

[In]

int(log(c*(d + e*x^n)^p)/(f + g*x),x)

[Out]

int(log(c*(d + e*x^n)^p)/(f + g*x), x)