3.616 \(\int \frac{F^{f (a+b \log (c (d+e x)^n))^2}}{(g+h x)^3} \, dx\)

Optimal. Leaf size=30 \[ \text{Unintegrable}\left (\frac{F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0993224, 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 = {} \[ \int \frac{F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 6.76969, size = 0, normalized size = 0. \[ \int \frac{F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.786, size = 0, normalized size = 0. \begin{align*} \int{\frac{{F}^{f \left ( a+b\ln \left ( c \left ( ex+d \right ) ^{n} \right ) \right ) ^{2}}}{ \left ( hx+g \right ) ^{3}}}\, 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)^3,x)

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{2} f}}{{\left (h x + g\right )}^{3}}\,{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)^3,x, algorithm="maxima")

[Out]

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

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{F^{b^{2} f \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + 2 \, a b f \log \left ({\left (e x + d\right )}^{n} c\right ) + a^{2} f}}{h^{3} x^{3} + 3 \, g h^{2} x^{2} + 3 \, g^{2} h x + g^{3}}, 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)^3,x, algorithm="fricas")

[Out]

integral(F^(b^2*f*log((e*x + d)^n*c)^2 + 2*a*b*f*log((e*x + d)^n*c) + a^2*f)/(h^3*x^3 + 3*g*h^2*x^2 + 3*g^2*h*
x + g^3), 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)**3,x)

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{2} f}}{{\left (h x + g\right )}^{3}}\,{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)^3,x, algorithm="giac")

[Out]

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