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

Optimal. Leaf size=28 \[ \text{Unintegrable}\left ((f+g x)^m \sqrt{a+b \log \left (c (d+e x)^n\right )},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0426145, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., 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*}

Mathematica [A]  time = 0.0637772, size = 0, normalized size = 0. \[ \int (f+g x)^m \sqrt{a+b \log \left (c (d+e x)^n\right )} \, dx \]

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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Maple [A]  time = 0.812, size = 0, normalized size = 0. \begin{align*} \int \left ( gx+f \right ) ^{m}\sqrt{a+b\ln \left ( c \left ( ex+d \right ) ^{n} \right ) }\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{b \log \left ({\left (e x + d\right )}^{n} c\right ) + a}{\left (g x + f\right )}^{m}\,{d x} \end{align*}

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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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\sqrt{b \log \left ({\left (e x + d\right )}^{n} c\right ) + a}{\left (g x + f\right )}^{m}, x\right ) \end{align*}

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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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

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]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{b \log \left ({\left (e x + d\right )}^{n} c\right ) + a}{\left (g x + f\right )}^{m}\,{d x} \end{align*}

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)