\(\int f^{\frac {c}{(a+b x)^2}} x^m \, dx\) [244]

Optimal result

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

[Out]

CannotIntegrate(f^(c/(b*x+a)^2)*x^m,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 = {} \[ \int f^{\frac {c}{(a+b x)^2}} x^m \, dx=\int f^{\frac {c}{(a+b x)^2}} x^m \, dx \]

[In]

Int[f^(c/(a + b*x)^2)*x^m,x]

[Out]

Defer[Int][f^(c/(a + b*x)^2)*x^m, x]

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

Mathematica [N/A]

Not integrable

Time = 0.07 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13 \[ \int f^{\frac {c}{(a+b x)^2}} x^m \, dx=\int f^{\frac {c}{(a+b x)^2}} x^m \, dx \]

[In]

Integrate[f^(c/(a + b*x)^2)*x^m,x]

[Out]

Integrate[f^(c/(a + b*x)^2)*x^m, x]

Maple [N/A]

Not integrable

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

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.28 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.87 \[ \int f^{\frac {c}{(a+b x)^2}} x^m \, dx=\int { f^{\frac {c}{{\left (b x + a\right )}^{2}}} x^{m} \,d x } \]

[In]

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

[Out]

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

Sympy [N/A]

Not integrable

Time = 38.29 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int f^{\frac {c}{(a+b x)^2}} x^m \, dx=\int f^{\frac {c}{\left (a + b x\right )^{2}}} x^{m}\, dx \]

[In]

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

[Out]

Integral(f**(c/(a + b*x)**2)*x**m, x)

Maxima [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13 \[ \int f^{\frac {c}{(a+b x)^2}} x^m \, dx=\int { f^{\frac {c}{{\left (b x + a\right )}^{2}}} x^{m} \,d x } \]

[In]

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

[Out]

integrate(f^(c/(b*x + a)^2)*x^m, x)

Giac [N/A]

Not integrable

Time = 0.40 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13 \[ \int f^{\frac {c}{(a+b x)^2}} x^m \, dx=\int { f^{\frac {c}{{\left (b x + a\right )}^{2}}} x^{m} \,d x } \]

[In]

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

[Out]

integrate(f^(c/(b*x + a)^2)*x^m, x)

Mupad [N/A]

Not integrable

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

[In]

int(f^(c/(a + b*x)^2)*x^m,x)

[Out]

int(f^(c/(a + b*x)^2)*x^m, x)