3.6.80 \(\int (a+b \log (c (d+e x^{2/3})^2))^p \, dx\) [580]

Optimal. Leaf size=23 \[ \text {Int}\left (\left (a+b \log \left (c \left (d+e x^{2/3}\right )^2\right )\right )^p,x\right ) \]

[Out]

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

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 0.07, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a+b \log \left (c \left (d+e x^{2/3}\right )^2\right )\right )^p \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

integral((b*log(2*c*d*x^(2/3)*e + c*x^(4/3)*e^2 + c*d^2) + a)^p, 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))**2))**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((a+b*log(c*(d+e*x^(2/3))^2))^p,x, algorithm="giac")

[Out]

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

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

[Out]

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

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