\(\int \frac {f^{c (a+b x)^n}}{x^2} \, dx\) [252]

Optimal result

Integrand size = 15, antiderivative size = 15 \[ \int \frac {f^{c (a+b x)^n}}{x^2} \, dx=\text {Int}\left (\frac {f^{c (a+b x)^n}}{x^2},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.03 (sec) , antiderivative size = 15, 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 = {} \[ \int \frac {f^{c (a+b x)^n}}{x^2} \, dx=\int \frac {f^{c (a+b x)^n}}{x^2} \, dx \]

[In]

Int[f^(c*(a + b*x)^n)/x^2,x]

[Out]

Defer[Int][f^(c*(a + b*x)^n)/x^2, x]

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

Mathematica [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13 \[ \int \frac {f^{c (a+b x)^n}}{x^2} \, dx=\int \frac {f^{c (a+b x)^n}}{x^2} \, dx \]

[In]

Integrate[f^(c*(a + b*x)^n)/x^2,x]

[Out]

Integrate[f^(c*(a + b*x)^n)/x^2, x]

Maple [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.28 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13 \[ \int \frac {f^{c (a+b x)^n}}{x^2} \, dx=\int { \frac {f^{{\left (b x + a\right )}^{n} c}}{x^{2}} \,d x } \]

[In]

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

[Out]

integral(f^((b*x + a)^n*c)/x^2, x)

Sympy [N/A]

Not integrable

Time = 0.44 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {f^{c (a+b x)^n}}{x^2} \, dx=\int \frac {f^{c \left (a + b x\right )^{n}}}{x^{2}}\, dx \]

[In]

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

[Out]

Integral(f**(c*(a + b*x)**n)/x**2, x)

Maxima [N/A]

Not integrable

Time = 0.23 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13 \[ \int \frac {f^{c (a+b x)^n}}{x^2} \, dx=\int { \frac {f^{{\left (b x + a\right )}^{n} c}}{x^{2}} \,d x } \]

[In]

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

[Out]

integrate(f^((b*x + a)^n*c)/x^2, x)

Giac [N/A]

Not integrable

Time = 0.37 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13 \[ \int \frac {f^{c (a+b x)^n}}{x^2} \, dx=\int { \frac {f^{{\left (b x + a\right )}^{n} c}}{x^{2}} \,d x } \]

[In]

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

[Out]

integrate(f^((b*x + a)^n*c)/x^2, x)

Mupad [N/A]

Not integrable

Time = 0.14 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13 \[ \int \frac {f^{c (a+b x)^n}}{x^2} \, dx=\int \frac {f^{c\,{\left (a+b\,x\right )}^n}}{x^2} \,d x \]

[In]

int(f^(c*(a + b*x)^n)/x^2,x)

[Out]

int(f^(c*(a + b*x)^n)/x^2, x)