3.153 \(\int \frac{x^3}{\log ^2(c (d+e x^3)^p)} \, dx\)

Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{x^3}{\log ^2\left (c \left (d+e x^3\right )^p\right )},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0173569, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{x^3}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \]

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*}

Mathematica [A]  time = 0.332326, size = 0, normalized size = 0. \[ \int \frac{x^3}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \]

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 = 3.507, size = 0, normalized size = 0. \begin{align*} \int{\frac{{x}^{3}}{ \left ( \ln \left ( c \left ( e{x}^{3}+d \right ) ^{p} \right ) \right ) ^{2}}}\, dx \end{align*}

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., size = 0, normalized size = 0. \begin{align*} -\frac{e x^{4} + d x}{3 \,{\left (e p \log \left ({\left (e x^{3} + d\right )}^{p}\right ) + e p \log \left (c\right )\right )}} + \int \frac{4 \, e x^{3} + d}{3 \,{\left (e p \log \left ({\left (e x^{3} + d\right )}^{p}\right ) + e p \log \left (c\right )\right )}}\,{d x} \end{align*}

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., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{x^{3}}{\log \left ({\left (e x^{3} + d\right )}^{p} c\right )^{2}}, x\right ) \end{align*}

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((e*x^3 + d)^p*c)^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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

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((e*x^3 + d)^p*c)^2, x)