3.4.27 \(\int \frac {1}{(d+e x^3)^2 (a+b \log (c x^n))} \, dx\) [327]

Optimal. Leaf size=25 \[ \text {Int}\left (\frac {1}{\left (d+e x^3\right )^2 \left (a+b \log \left (c x^n\right )\right )},x\right ) \]

[Out]

Unintegrable(1/(e*x^3+d)^2/(a+b*ln(c*x^n)),x)

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Rubi [A]
time = 0.02, 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}{\left (d+e x^3\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/((d + e*x^3)^2*(a + b*Log[c*x^n])),x]

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 4.05, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (d+e x^3\right )^2 \left (a+b \log \left (c x^n\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 0.04, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (e \,x^{3}+d \right )^{2} \left (a +b \ln \left (c \,x^{n}\right )\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(1/(e*x^3+d)^2/(a+b*ln(c*x^n)),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/(e*x^3+d)^2/(a+b*log(c*x^n)),x, algorithm="maxima")

[Out]

integrate(1/((x^3*e + d)^2*(b*log(c*x^n) + a)), 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(1/(e*x^3+d)^2/(a+b*log(c*x^n)),x, algorithm="fricas")

[Out]

integral(1/(a*x^6*e^2 + 2*a*d*x^3*e + a*d^2 + (b*x^6*e^2 + 2*b*d*x^3*e + b*d^2)*log(c*x^n)), x)

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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x**3+d)**2/(a+b*ln(c*x**n)),x)

[Out]

Timed out

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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/(e*x^3+d)^2/(a+b*log(c*x^n)),x, algorithm="giac")

[Out]

integrate(1/((x^3*e + d)^2*(b*log(c*x^n) + a)), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {1}{{\left (e\,x^3+d\right )}^2\,\left (a+b\,\ln \left (c\,x^n\right )\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((d + e*x^3)^2*(a + b*log(c*x^n))),x)

[Out]

int(1/((d + e*x^3)^2*(a + b*log(c*x^n))), x)

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