\(\int \frac {F^{f (a+b \log ^2(c (d+e x)^n))}}{g+h x} \, dx\) [599]

Optimal result

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

[Out]

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

[In]

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

[Out]

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

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

Mathematica [N/A]

Not integrable

Time = 0.63 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{g+h x} \, dx=\int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{g+h x} \, dx \]

[In]

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

[Out]

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

Maple [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.11 \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{g+h x} \, dx=\int { \frac {F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + a\right )} f}}{h x + g} \,d x } \]

[In]

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

[Out]

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

Sympy [N/A]

Not integrable

Time = 8.12 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86 \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{g+h x} \, dx=\int \frac {F^{f \left (a + b \log {\left (c \left (d + e x\right )^{n} \right )}^{2}\right )}}{g + h x}\, dx \]

[In]

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

[Out]

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

Maxima [N/A]

Not integrable

Time = 0.53 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{g+h x} \, dx=\int { \frac {F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + a\right )} f}}{h x + g} \,d x } \]

[In]

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

[Out]

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

Giac [N/A]

Not integrable

Time = 0.48 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{g+h x} \, dx=\int { \frac {F^{{\left (b \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + a\right )} f}}{h x + g} \,d x } \]

[In]

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

[Out]

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

Mupad [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.11 \[ \int \frac {F^{f \left (a+b \log ^2\left (c (d+e x)^n\right )\right )}}{g+h x} \, dx=\int \frac {{\mathrm {e}}^{f\,\ln \left (F\right )\,\left (b\,{\ln \left (c\,{\left (d+e\,x\right )}^n\right )}^2+a\right )}}{g+h\,x} \,d x \]

[In]

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

[Out]

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