3.3.11 \(\int (f+g x)^m \log (c (d+e x^n)^p) \, dx\) [211]

Optimal. Leaf size=23 \[ \text {Int}\left ((f+g x)^m \log \left (c \left (d+e x^n\right )^p\right ),x\right ) \]

[Out]

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

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*}

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Mathematica [A]
time = 0.36, size = 0, normalized size = 0.00 \begin {gather*} \int (f+g x)^m \log \left (c \left (d+e x^n\right )^p\right ) \, dx \end {gather*}

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 = 0.26, size = 0, normalized size = 0.00 \[\int \left (g x +f \right )^{m} \ln \left (c \left (d +e \,x^{n}\right )^{p}\right )\, dx\]

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 [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

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]

(g*x + f)*(g*x + f)^m*log((d + e^(n*log(x) + 1))^p)/(g*(m + 1)) + integrate((d*g*(m + 1)*x*log(c) - (f*n*p*e +
(g*n*p - g*(m + 1)*log(c))*x*e)*x^n)*(g*x + f)^m/(d*g*(m + 1)*x + g*(m + 1)*x*e^(n*log(x) + 1)), x)

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

[Out]

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

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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

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 = 0.00, 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*log(c*(d+e*x^n)^p),x, algorithm="giac")

[Out]

Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Simplification as
suming sageVARf near 0Unable to divide, perhaps due to rounding error%%%{-1,[0,0,6,3,6,0,2,2,0,1,0]%%%}+%%%{1,
[0,0,6,2,6,1,2

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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