3.2.65 \(\int (f+g x)^m (a+b \log (c (d+e x)^n))^{3/2} \, dx\) [165]

Optimal. Leaf size=29 \[ \text {Int}\left ((f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2},x\right ) \]

[Out]

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

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Rubi [A]
time = 0.03, 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 (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 14.76, size = 0, normalized size = 0.00 \begin {gather*} \int (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 0.16, size = 0, normalized size = 0.00 \[\int \left (g x +f \right )^{m} \left (a +b \ln \left (c \left (e x +d \right )^{n}\right )\right )^{\frac {3}{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

integral(((g*x + f)^m*b*log((x*e + d)^n*c) + (g*x + f)^m*a)*sqrt(b*log((x*e + d)^n*c) + a), 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((g*x+f)**m*(a+b*ln(c*(e*x+d)**n))**(3/2),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((g*x+f)^m*(a+b*log(c*(e*x+d)^n))^(3/2),x, algorithm="giac")

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int {\left (f+g\,x\right )}^m\,{\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )}^{3/2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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