3.240 \(\int f^{c (a+b x)^3} x^m \, dx\)

Optimal. Leaf size=18 \[ \text {Int}\left (x^m f^{c (a+b x)^3},x\right ) \]

[Out]

CannotIntegrate(f^(c*(b*x+a)^3)*x^m,x)

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Rubi [A]  time = 0.05, 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 = {} \[ \int f^{c (a+b x)^3} x^m \, dx \]

Verification is Not applicable to the result.

[In]

Int[f^(c*(a + b*x)^3)*x^m,x]

[Out]

Defer[Int][f^(c*(a + b*x)^3)*x^m, x]

Rubi steps

\begin {align*} \int f^{c (a+b x)^3} x^m \, dx &=\int f^{c (a+b x)^3} x^m \, dx\\ \end {align*}

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Mathematica [A]  time = 0.25, size = 0, normalized size = 0.00 \[ \int f^{c (a+b x)^3} x^m \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[f^(c*(a + b*x)^3)*x^m,x]

[Out]

Integrate[f^(c*(a + b*x)^3)*x^m, x]

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fricas [A]  time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (f^{b^{3} c x^{3} + 3 \, a b^{2} c x^{2} + 3 \, a^{2} b c x + a^{3} c} x^{m}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(f^(c*(b*x+a)^3)*x^m,x, algorithm="fricas")

[Out]

integral(f^(b^3*c*x^3 + 3*a*b^2*c*x^2 + 3*a^2*b*c*x + a^3*c)*x^m, x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int f^{{\left (b x + a\right )}^{3} c} x^{m}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(f^(c*(b*x+a)^3)*x^m,x, algorithm="giac")

[Out]

integrate(f^((b*x + a)^3*c)*x^m, x)

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maple [A]  time = 0.06, size = 0, normalized size = 0.00 \[ \int f^{\left (b x +a \right )^{3} c} x^{m}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(f^((b*x+a)^3*c)*x^m,x)

[Out]

int(f^((b*x+a)^3*c)*x^m,x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int f^{{\left (b x + a\right )}^{3} c} x^{m}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(f^(c*(b*x+a)^3)*x^m,x, algorithm="maxima")

[Out]

integrate(f^((b*x + a)^3*c)*x^m, x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int f^{c\,{\left (a+b\,x\right )}^3}\,x^m \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(f^(c*(a + b*x)^3)*x^m,x)

[Out]

int(f^(c*(a + b*x)^3)*x^m, x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int f^{c \left (a + b x\right )^{3}} x^{m}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(f**(c*(b*x+a)**3)*x**m,x)

[Out]

Integral(f**(c*(a + b*x)**3)*x**m, x)

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