3.174 \(\int \frac{(a+b \log (c (d+e x)^n))^n}{f+g x} \, dx\)

Optimal. Leaf size=26 \[ \text{Unintegrable}\left (\frac{\left (a+b \log \left (c (d+e x)^n\right )\right )^n}{f+g x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0293431, 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 = {} \[ \int \frac{\left (a+b \log \left (c (d+e x)^n\right )\right )^n}{f+g x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.252056, size = 0, normalized size = 0. \[ \int \frac{\left (a+b \log \left (c (d+e x)^n\right )\right )^n}{f+g x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 1.052, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( a+b\ln \left ( c \left ( ex+d \right ) ^{n} \right ) \right ) ^{n}}{gx+f}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int((a+b*ln(c*(e*x+d)^n))^n/(g*x+f),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((a+b*log(c*(e*x+d)^n))^n/(g*x+f),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{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{n}}{g x + f}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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