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

Optimal. Leaf size=19 \[ \text {Int}\left (\frac {x}{\log ^2\left (c \left (d+e x^3\right )^p\right )},x\right ) \]

[Out]

Unintegrable(x/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 = {} \[ \int \frac {x}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[x/Log[c*(d + e*x^3)^p]^2,x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.50, size = 0, normalized size = 0.00 \[ \int \frac {x}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[x/Log[c*(d + e*x^3)^p]^2,x]

[Out]

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

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fricas [A]  time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {x}{\log \left ({\left (e x^{3} + d\right )}^{p} c\right )^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(x/log((e*x^3 + d)^p*c)^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 4.05, size = 0, normalized size = 0.00 \[ \int \frac {x}{\ln \left (c \left (e \,x^{3}+d \right )^{p}\right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x/log(c*(d + e*x^3)^p)^2,x)

[Out]

int(x/log(c*(d + e*x^3)^p)^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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