3.6.71 \(\int \frac {(a+b \log (c (d+e x^{2/3})))^p}{x^3} \, dx\) [571]

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

[Out]

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

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Rubi [A]
time = 0.04, 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 {\left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p}{x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x^2)])^p/x^7, x], x, x^(1/3)]

Rubi steps

\begin {align*} \int \frac {\left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p}{x^3} \, dx &=3 \text {Subst}\left (\int \frac {\left (a+b \log \left (c \left (d+e x^2\right )\right )\right )^p}{x^7} \, dx,x,\sqrt [3]{x}\right )\\ \end {align*}

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Mathematica [A]
time = 0.47, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p}{x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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