3.2.69 \(\int (f+g x)^m (a+b \log (c (d+e x)^n))^n \, dx\) [169]

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

[Out]

Unintegrable((g*x+f)^m*(a+b*ln(c*(e*x+d)^n))^n,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 (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^n \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 0.29, size = 0, normalized size = 0.00 \begin {gather*} \int (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^n \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 0.16, size = 0, normalized size = 0.00 \[\int \left (g x +f \right )^{m} \left (a +b \ln \left (c \left (e x +d \right )^{n}\right )\right )^{n}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: HeuristicGCDFailed} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

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

[Out]

Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Simplification as
suming sageVARd near 0Simplification assuming sageVARd near 0Simplification assuming sageVARd near 0Simplifica
tion assuming

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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