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

Optimal. Leaf size=31 \[ \text{Unintegrable}\left (\frac{\log ^q\left (c \left (d+e x^n\right )^p\right )}{x \left (f+g x^{-n}\right )},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.10548, 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 = {} \[ \int \frac{\log ^q\left (c \left (d+e x^n\right )^p\right )}{x \left (f+g x^{-n}\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 1.80261, size = 0, normalized size = 0. \[ \int \frac{\log ^q\left (c \left (d+e x^n\right )^p\right )}{x \left (f+g x^{-n}\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 21.518, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \ln \left ( c \left ( d+e{x}^{n} \right ) ^{p} \right ) \right ) ^{q}}{x} \left ( f+{\frac{g}{{x}^{n}}} \right ) ^{-1}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: RuntimeError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: RuntimeError

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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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 )^{q}}{{\left (f + \frac{g}{x^{n}}\right )} x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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