3.2.51 \(\int \frac {1}{x \log ^2(c (d+e x^3)^p)} \, dx\) [151]

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {1}{x \log ^2\left (c \left (d+e x^3\right )^p\right )},x\right ) \]

[Out]

Unintegrable(1/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 = {} \begin {gather*} \int \frac {1}{x \log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/(x*Log[c*(d + e*x^3)^p]^2),x]

[Out]

Defer[Int][1/(x*Log[c*(d + e*x^3)^p]^2), x]

Rubi steps

\begin {align*} \int \frac {1}{x \log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx &=\int \frac {1}{x \log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx\\ \end {align*}

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Mathematica [A]
time = 0.20, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x \log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[1/(x*Log[c*(d + e*x^3)^p]^2),x]

[Out]

Integrate[1/(x*Log[c*(d + e*x^3)^p]^2), x]

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Maple [A]
time = 0.00, size = 0, normalized size = 0.00 \[\int \frac {1}{x \ln \left (c \left (e \,x^{3}+d \right )^{p}\right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x/ln(c*(e*x^3+d)^p)^2,x)

[Out]

int(1/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 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

[Out]

integral(1/(x*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 {1}{x \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(1/x/ln(c*(e*x**3+d)**p)**2,x)

[Out]

Integral(1/(x*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(1/x/log(c*(e*x^3+d)^p)^2,x, algorithm="giac")

[Out]

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

[Out]

int(1/(x*log(c*(d + e*x^3)^p)^2), x)

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