3.199 \(\int \frac {f^{c (a+b x)^2}}{x} \, dx\)

Optimal. Leaf size=18 \[ \text {Int}\left (\frac {f^{c (a+b x)^2}}{x},x\right ) \]

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.03, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {f^{c (a+b x)^2}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[f^(c*(a + b*x)^2)/x,x]

[Out]

Defer[Int][f^(c*(a + b*x)^2)/x, x]

Rubi steps

\begin {align*} \int \frac {f^{c (a+b x)^2}}{x} \, dx &=\int \frac {f^{c (a+b x)^2}}{x} \, dx\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.12, size = 0, normalized size = 0.00 \[ \int \frac {f^{c (a+b x)^2}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[f^(c*(a + b*x)^2)/x,x]

[Out]

Integrate[f^(c*(a + b*x)^2)/x, x]

________________________________________________________________________________________

fricas [A]  time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {f^{b^{2} c x^{2} + 2 \, a b c x + a^{2} c}}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {f^{{\left (b x + a\right )}^{2} c}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(f^((b*x + a)^2*c)/x, x)

________________________________________________________________________________________

maple [A]  time = 0.04, size = 0, normalized size = 0.00 \[ \int \frac {f^{\left (b x +a \right )^{2} c}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {f^{{\left (b x + a\right )}^{2} c}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(f^((b*x + a)^2*c)/x, x)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {f^{c\,{\left (a+b\,x\right )}^2}}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(f^(c*(a + b*x)^2)/x,x)

[Out]

int(f^(c*(a + b*x)^2)/x, x)

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {f^{c \left (a + b x\right )^{2}}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(f**(c*(a + b*x)**2)/x, x)

________________________________________________________________________________________