3.594 \(\int F^{f (a+b \log ^2(c (d+e x)^n))} (g+h x)^m \, dx\)

Optimal. Leaf size=30 \[ \text{Unintegrable}\left ((g+h x)^m F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )},x\right ) \]

[Out]

Unintegrable[F^(f*(a + b*Log[c*(d + e*x)^n]^2))*(g + h*x)^m, x]

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Rubi [A]  time = 0.0762954, 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 = {} \[ \int F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )} (g+h x)^m \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 1.77503, size = 0, normalized size = 0. \[ \int F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )} (g+h x)^m \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.861, size = 0, normalized size = 0. \begin{align*} \int{F}^{f \left ( a+b \left ( \ln \left ( c \left ( ex+d \right ) ^{n} \right ) \right ) ^{2} \right ) } \left ( hx+g \right ) ^{m}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (h x + g\right )}^{m} F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + a\right )} f}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left ({\left (h x + g\right )}^{m} F^{b f \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + a f}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral((h*x + g)^m*F^(b*f*log((e*x + d)^n*c)^2 + a*f), 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(F**(f*(a+b*ln(c*(e*x+d)**n)**2))*(h*x+g)**m,x)

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (h x + g\right )}^{m} F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + a\right )} f}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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