3.2.74 \(\int \frac {(a+b \log (c (d+e x)^n))^n}{f+g x} \, dx\) [174]

Optimal. Leaf size=27 \[ \text {Int}\left (\frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^n}{f+g x},x\right ) \]

[Out]

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

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Rubi [A]
time = 0.02, 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 = {} \begin {gather*} \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^n}{f+g x} \, dx \end {gather*}

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*}

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Mathematica [A]
time = 0.15, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^n}{f+g x} \, dx \end {gather*}

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 = 0.17, size = 0, normalized size = 0.00 \[\int \frac {\left (a +b \ln \left (c \left (e x +d \right )^{n}\right )\right )^{n}}{g x +f}\, dx\]

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}

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 >> ECL says: In function CAR, the value of the first argument is  0which is not
of the expected type LIST

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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((x*e + d)^n*c) + a)^n/(g*x + f), x)

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

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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((x*e + d)^n*c) + a)^n/(g*x + f), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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