3.211 \(\int (f+g x)^m \log (c (d+e x^n)^p) \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.0110441, 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 = {} \[ \int (f+g x)^m \log \left (c \left (d+e x^n\right )^p\right ) \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.523136, size = 0, normalized size = 0. \[ \int (f+g x)^m \log \left (c \left (d+e x^n\right )^p\right ) \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 2.648, size = 0, normalized size = 0. \begin{align*} \int \left ( gx+f \right ) ^{m}\ln \left ( c \left ( d+e{x}^{n} \right ) ^{p} \right ) \, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: ValueError

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

Timed out

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Giac [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((g*x+f)^m*log(c*(d+e*x^n)^p),x, algorithm="giac")

[Out]

Exception raised: RuntimeError