3.2.53 \(\int \frac {x^3}{\log ^2(c (d+e x^3)^p)} \, dx\) [153]

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {x^3}{\log ^2\left (c \left (d+e x^3\right )^p\right )},x\right ) \]

[Out]

Unintegrable(x^3/ln(c*(e*x^3+d)^p)^2,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 {x^3}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[x^3/Log[c*(d + e*x^3)^p]^2,x]

[Out]

Defer[Int][x^3/Log[c*(d + e*x^3)^p]^2, x]

Rubi steps

\begin {align*} \int \frac {x^3}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx &=\int \frac {x^3}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx\\ \end {align*}

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Mathematica [A]
time = 0.23, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^3}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[x^3/Log[c*(d + e*x^3)^p]^2,x]

[Out]

Integrate[x^3/Log[c*(d + e*x^3)^p]^2, x]

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Maple [A]
time = 0.00, size = 0, normalized size = 0.00 \[\int \frac {x^{3}}{\ln \left (c \left (e \,x^{3}+d \right )^{p}\right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^3/ln(c*(e*x^3+d)^p)^2,x)

[Out]

int(x^3/ln(c*(e*x^3+d)^p)^2,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(x^3/log(c*(e*x^3+d)^p)^2,x, algorithm="maxima")

[Out]

-1/3*(e*x^4 + d*x)/(e*p*log((e*x^3 + d)^p) + e*p*log(c)) + integrate(1/3*(4*e*x^3 + d)/(e*p*log((e*x^3 + d)^p)
+ e*p*log(c)), 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(x^3/log(c*(e*x^3+d)^p)^2,x, algorithm="fricas")

[Out]

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

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^{3}}{\log {\left (c \left (d + e x^{3}\right )^{p} \right )}^{2}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**3/ln(c*(e*x**3+d)**p)**2,x)

[Out]

Integral(x**3/log(c*(d + e*x**3)**p)**2, 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(x^3/log(c*(e*x^3+d)^p)^2,x, algorithm="giac")

[Out]

integrate(x^3/log((x^3*e + d)^p*c)^2, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {x^3}{{\ln \left (c\,{\left (e\,x^3+d\right )}^p\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^3/log(c*(d + e*x^3)^p)^2,x)

[Out]

int(x^3/log(c*(d + e*x^3)^p)^2, x)

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