3.6.72 \(\int x^2 (a+b \log (c (d+e x^{2/3})))^p \, dx\) [572]

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

[Out]

Unintegrable(x^2*(a+b*ln(c*(d+e*x^(2/3))))^p,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 x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

3*Defer[Subst][Defer[Int][x^8*(a + b*Log[c*(d + e*x^2)])^p, x], x, x^(1/3)]

Rubi steps

\begin {align*} \int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p \, dx &=3 \text {Subst}\left (\int x^8 \left (a+b \log \left (c \left (d+e x^2\right )\right )\right )^p \, dx,x,\sqrt [3]{x}\right )\\ \end {align*}

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Mathematica [A]
time = 0.60, size = 0, normalized size = 0.00 \begin {gather*} \int x^2 \left (a+b \log \left (c \left (d+e x^{2/3}\right )\right )\right )^p \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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