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

Optimal. Leaf size=29 \[ \text{Unintegrable}\left (\frac{\log ^q\left (c \left (d+e x^n\right )^p\right )}{x \left (f+g x^n\right )},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0861844, 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 = 1.75876, 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 = 19.992, 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+g{x}^{n} \right ) }}\, 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{\log \left ({\left (e x^{n} + d\right )}^{p} c\right )^{q}}{g x x^{n} + f 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(log((e*x^n + d)^p*c)^q/(g*x*x^n + f*x), 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 )}^{q}}{x \left (f + g x^{n}\right )}\, dx \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]

Integral(log(c*(d + e*x**n)**p)**q/(x*(f + g*x**n)), 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 )^{q}}{{\left (g x^{n} + f\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/((g*x^n + f)*x), x)