3.3.18 \(\int \frac {\log (c (d+e x^n)^p)}{(f+g x)^3} \, dx\) [218]

Optimal. Leaf size=23 \[ \text {Int}\left (\frac {\log \left (c \left (d+e x^n\right )^p\right )}{(f+g x)^3},x\right ) \]

[Out]

Unintegrable(ln(c*(d+e*x^n)^p)/(g*x+f)^3,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 \frac {\log \left (c \left (d+e x^n\right )^p\right )}{(f+g x)^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Log[c*(d + e*x^n)^p]/(f + g*x)^3,x]

[Out]

Defer[Int][Log[c*(d + e*x^n)^p]/(f + g*x)^3, x]

Rubi steps

\begin {align*} \int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{(f+g x)^3} \, dx &=\int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{(f+g x)^3} \, dx\\ \end {align*}

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Mathematica [A]
time = 0.19, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{(f+g x)^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Log[c*(d + e*x^n)^p]/(f + g*x)^3,x]

[Out]

Integrate[Log[c*(d + e*x^n)^p]/(f + g*x)^3, x]

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Maple [A]
time = 0.22, size = 0, normalized size = 0.00 \[\int \frac {\ln \left (c \left (d +e \,x^{n}\right )^{p}\right )}{\left (g x +f \right )^{3}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(c*(d+e*x^n)^p)/(g*x+f)^3,x)

[Out]

int(ln(c*(d+e*x^n)^p)/(g*x+f)^3,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(log(c*(d+e*x^n)^p)/(g*x+f)^3,x, algorithm="maxima")

[Out]

-d*n*p*integrate(1/2/(d*g^3*x^3 + 2*d*f*g^2*x^2 + d*f^2*g*x + (g^3*x^3*e + 2*f*g^2*x^2*e + f^2*g*x*e)*x^n), x)
+ 1/2*(f*g*n*p*x + f^2*n*p - f^2*log(c) - f^2*log((d + e^(n*log(x) + 1))^p) + (g^2*n*p*x^2 + 2*f*g*n*p*x + f^
2*n*p)*log(x))/(f^2*g^3*x^2 + 2*f^3*g^2*x + f^4*g) - 1/2*n*p*log(g*x + f)/(f^2*g)

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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(log(c*(d+e*x^n)^p)/(g*x+f)^3,x, algorithm="fricas")

[Out]

integral(log((x^n*e + d)^p*c)/(g^3*x^3 + 3*f*g^2*x^2 + 3*f^2*g*x + f^3), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\log {\left (c \left (d + e x^{n}\right )^{p} \right )}}{\left (f + g x\right )^{3}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(c*(d+e*x**n)**p)/(g*x+f)**3,x)

[Out]

Integral(log(c*(d + e*x**n)**p)/(f + g*x)**3, 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(log(c*(d+e*x^n)^p)/(g*x+f)^3,x, algorithm="giac")

[Out]

integrate(log((x^n*e + d)^p*c)/(g*x + f)^3, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {\ln \left (c\,{\left (d+e\,x^n\right )}^p\right )}{{\left (f+g\,x\right )}^3} \,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)^3,x)

[Out]

int(log(c*(d + e*x^n)^p)/(f + g*x)^3, x)

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