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

Optimal. Leaf size=29 \[ \text {Int}\left (x^m f^{a^2 c+2 a b c x+b^2 c x^2},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.06, 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 = {} \[ \int f^{c (a+b x)^2} x^m \, dx \]

Verification is Not applicable to the result.

[In]

Int[f^(c*(a + b*x)^2)*x^m,x]

[Out]

Defer[Int][f^(a^2*c + 2*a*b*c*x + b^2*c*x^2)*x^m, x]

Rubi steps

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

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Mathematica [A]  time = 0.15, size = 0, normalized size = 0.00 \[ \int f^{c (a+b x)^2} x^m \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[f^(c*(a + b*x)^2)*x^m,x]

[Out]

Integrate[f^(c*(a + b*x)^2)*x^m, x]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(f^((b*x + a)^2*c)*x^m, x)

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maple [A]  time = 0.06, size = 0, normalized size = 0.00 \[ \int f^{\left (b x +a \right )^{2} c} x^{m}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(f^((b*x + a)^2*c)*x^m, x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.03 \[ \int f^{c\,{\left (a+b\,x\right )}^2}\,x^m \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(f^(c*(a + b*x)^2)*x^m,x)

[Out]

int(f^(c*(a + b*x)^2)*x^m, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(f**(c*(a + b*x)**2)*x**m, x)

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