\(\int \frac {F^{f (a+b \log (c (d+e x)^n))^2}}{(g+h x)^3} \, dx\) [616]

Optimal result

Integrand size = 28, antiderivative size = 28 \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx=\text {Int}\left (\frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx=\int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx \]

[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*} \text {integral}& = \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 [N/A]

Not integrable

Time = 3.50 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx=\int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx \]

[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]

Maple [N/A]

Not integrable

Time = 0.04 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00

\[\int \frac {F^{f {\left (a +b \ln \left (c \left (e x +d \right )^{n}\right )\right )}^{2}}}{\left (h x +g \right )^{3}}d x\]

[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)

Fricas [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.57 \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx=\int { \frac {F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{2} f}}{{\left (h x + g\right )}^{3}} \,d x } \]

[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)

Sympy [N/A]

Not integrable

Time = 0.00 (sec) , antiderivative size = 1, normalized size of antiderivative = 0.04 \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx=\int \frac {F^{f \left (a + b \log {\left (c \left (d + e x\right )^{n} \right )}\right )^{2}}}{\left (g + h x\right )^{3}} \, dx \]

[In]

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

[Out]

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

Maxima [N/A]

Not integrable

Time = 0.79 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx=\int { \frac {F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{2} f}}{{\left (h x + g\right )}^{3}} \,d x } \]

[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)

Giac [N/A]

Not integrable

Time = 0.66 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx=\int { \frac {F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{2} f}}{{\left (h x + g\right )}^{3}} \,d x } \]

[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)

Mupad [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.11 \[ \int \frac {F^{f \left (a+b \log \left (c (d+e x)^n\right )\right )^2}}{(g+h x)^3} \, dx=\int \frac {{\mathrm {e}}^{f\,\ln \left (F\right )\,{\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )}^2}}{{\left (g+h\,x\right )}^3} \,d x \]

[In]

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

[Out]

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