\(\int \frac {f^{a+b x+c x^2}}{d+e x} \, dx\) [447]

Optimal result

Integrand size = 20, antiderivative size = 20 \[ \int \frac {f^{a+b x+c x^2}}{d+e x} \, dx=\text {Int}\left (\frac {f^{a+b x+c x^2}}{d+e x},x\right ) \]

[Out]

Unintegrable(f^(c*x^2+b*x+a)/(e*x+d),x)

Rubi [N/A]

Not integrable

Time = 0.03 (sec) , antiderivative size = 20, 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 = {} \[ \int \frac {f^{a+b x+c x^2}}{d+e x} \, dx=\int \frac {f^{a+b x+c x^2}}{d+e x} \, dx \]

[In]

Int[f^(a + b*x + c*x^2)/(d + e*x),x]

[Out]

Defer[Int][f^(a + b*x + c*x^2)/(d + e*x), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {f^{a+b x+c x^2}}{d+e x} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.33 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {f^{a+b x+c x^2}}{d+e x} \, dx=\int \frac {f^{a+b x+c x^2}}{d+e x} \, dx \]

[In]

Integrate[f^(a + b*x + c*x^2)/(d + e*x),x]

[Out]

Integrate[f^(a + b*x + c*x^2)/(d + e*x), x]

Maple [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00

\[\int \frac {f^{c \,x^{2}+b x +a}}{e x +d}d x\]

[In]

int(f^(c*x^2+b*x+a)/(e*x+d),x)

[Out]

int(f^(c*x^2+b*x+a)/(e*x+d),x)

Fricas [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {f^{a+b x+c x^2}}{d+e x} \, dx=\int { \frac {f^{c x^{2} + b x + a}}{e x + d} \,d x } \]

[In]

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

[Out]

integral(f^(c*x^2 + b*x + a)/(e*x + d), x)

Sympy [N/A]

Not integrable

Time = 0.34 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \frac {f^{a+b x+c x^2}}{d+e x} \, dx=\int \frac {f^{a + b x + c x^{2}}}{d + e x}\, dx \]

[In]

integrate(f**(c*x**2+b*x+a)/(e*x+d),x)

[Out]

Integral(f**(a + b*x + c*x**2)/(d + e*x), x)

Maxima [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {f^{a+b x+c x^2}}{d+e x} \, dx=\int { \frac {f^{c x^{2} + b x + a}}{e x + d} \,d x } \]

[In]

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

[Out]

integrate(f^(c*x^2 + b*x + a)/(e*x + d), x)

Giac [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {f^{a+b x+c x^2}}{d+e x} \, dx=\int { \frac {f^{c x^{2} + b x + a}}{e x + d} \,d x } \]

[In]

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

[Out]

integrate(f^(c*x^2 + b*x + a)/(e*x + d), x)

Mupad [N/A]

Not integrable

Time = 0.43 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {f^{a+b x+c x^2}}{d+e x} \, dx=\int \frac {f^{c\,x^2+b\,x+a}}{d+e\,x} \,d x \]

[In]

int(f^(a + b*x + c*x^2)/(d + e*x),x)

[Out]

int(f^(a + b*x + c*x^2)/(d + e*x), x)