3.166 \(\int (f+g x)^m \sqrt {a+b \log (c (d+e x)^n)} \, dx\)

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

[Out]

Unintegrable((g*x+f)^m*(a+b*ln(c*(e*x+d)^n))^(1/2),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 = {} \[ \int (f+g x)^m \sqrt {a+b \log \left (c (d+e x)^n\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.07, size = 0, normalized size = 0.00 \[ \int (f+g x)^m \sqrt {a+b \log \left (c (d+e x)^n\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\sqrt {b \log \left ({\left (e x + d\right )}^{n} c\right ) + a} {\left (g x + f\right )}^{m}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(sqrt(b*log((e*x + d)^n*c) + a)*(g*x + f)^m, x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \sqrt {b \log \left ({\left (e x + d\right )}^{n} c\right ) + a} {\left (g x + f\right )}^{m}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((g*x+f)^m*(a+b*log(c*(e*x+d)^n))^(1/2),x, algorithm="giac")

[Out]

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

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maple [A]  time = 0.64, size = 0, normalized size = 0.00 \[ \int \sqrt {b \ln \left (c \left (e x +d \right )^{n}\right )+a}\, \left (g x +f \right )^{m}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \sqrt {b \log \left ({\left (e x + d\right )}^{n} c\right ) + a} {\left (g x + f\right )}^{m}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((g*x+f)^m*(a+b*log(c*(e*x+d)^n))^(1/2),x, algorithm="maxima")

[Out]

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

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mupad [A]  time = 0.00, size = -1, normalized size = -0.03 \[ \int {\left (f+g\,x\right )}^m\,\sqrt {a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: HeuristicGCDFailed} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: HeuristicGCDFailed

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