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

Optimal. Leaf size=25 \[ \text {Int}\left (\left (a+b \log \left (c \left (d+\frac {e}{f+g x}\right )^p\right )\right )^n,x\right ) \]

[Out]

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

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Rubi [A]  time = 0.01, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (a+b \log \left (c \left (d+\frac {e}{f+g x}\right )^p\right )\right )^n \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.42, size = 0, normalized size = 0.00 \[ \int \left (a+b \log \left (c \left (d+\frac {e}{f+g x}\right )^p\right )\right )^n \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (b \log \left (c \left (\frac {d g x + d f + e}{g x + f}\right )^{p}\right ) + a\right )}^{n}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b \log \left (c {\left (d + \frac {e}{g x + f}\right )}^{p}\right ) + a\right )}^{n}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.30, size = 0, normalized size = 0.00 \[ \int \left (b \ln \left (c \left (d +\frac {e}{g x +f}\right )^{p}\right )+a \right )^{n}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b \log \left (c {\left (d + \frac {e}{g x + f}\right )}^{p}\right ) + a\right )}^{n}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int {\left (a+b\,\ln \left (c\,{\left (d+\frac {e}{f+g\,x}\right )}^p\right )\right )}^n \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (a + b \log {\left (c \left (d + \frac {e}{f + g x}\right )^{p} \right )}\right )^{n}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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