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

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

[Out]

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

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Rubi [A]  time = 0.04, 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 = {} \[ \int f^{\frac {c}{a+b x}} x^m \, dx \]

Verification is Not applicable to the result.

[In]

Int[f^(c/(a + b*x))*x^m,x]

[Out]

Defer[Int][f^(c/(a + b*x))*x^m, x]

Rubi steps

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

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Mathematica [A]  time = 0.05, size = 0, normalized size = 0.00 \[ \int f^{\frac {c}{a+b x}} x^m \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[f^(c/(a + b*x))*x^m,x]

[Out]

Integrate[f^(c/(a + b*x))*x^m, x]

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fricas [A]  time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (f^{\frac {c}{b x + a}} x^{m}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(f^(c/(b*x + a))*x^m, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(f^(c/(b*x + a))*x^m, x)

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maple [A]  time = 0.06, size = 0, normalized size = 0.00 \[ \int f^{\frac {c}{b x +a}} x^{m}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(f^(1/(b*x+a)*c)*x^m,x)

[Out]

int(f^(1/(b*x+a)*c)*x^m,x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(f^(c/(b*x + a))*x^m, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(f^(c/(a + b*x))*x^m,x)

[Out]

int(f^(c/(a + b*x))*x^m, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(f**(c/(a + b*x))*x**m, x)

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