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

Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{\log \left (c \left (d+e x^n\right )^p\right )}{f+g x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0124176, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\log \left (c \left (d+e x^n\right )^p\right )}{f+g x} \, dx \]

Verification is Not applicable to the result.

[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*} \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\\ \end{align*}

Mathematica [A]  time = 1.59032, size = 0, normalized size = 0. \[ \int \frac{\log \left (c \left (d+e x^n\right )^p\right )}{f+g x} \, dx \]

Verification is Not applicable to the result.

[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]

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Maple [A]  time = 2.352, size = 0, normalized size = 0. \begin{align*} \int{\frac{\ln \left ( c \left ( d+e{x}^{n} \right ) ^{p} \right ) }{gx+f}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log \left ({\left (e x^{n} + d\right )}^{p} c\right )}{g x + f}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\log \left ({\left (e x^{n} + d\right )}^{p} c\right )}{g x + f}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log{\left (c \left (d + e x^{n}\right )^{p} \right )}}{f + g x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log \left ({\left (e x^{n} + d\right )}^{p} c\right )}{g x + f}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[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)