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

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Rubi [A]  time = 0.0831965, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (f^{c (a+b x)^2} x^m,x\right ) \]

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]

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Rubi in Sympy [A]  time = 0., size = 0, normalized size = 0. \[ \int f^{a^{2} c + 2 a b c x + b^{2} c x^{2}} x^{m}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(f**(c*(b*x+a)**2)*x**m,x)

[Out]

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

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Mathematica [A]  time = 0.195754, size = 0, normalized size = 0. \[ \int f^{c (a+b x)^2} x^m \, dx \]

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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Maple [A]  time = 0.041, size = 0, normalized size = 0. \[ \int{f}^{c \left ( bx+a \right ) ^{2}}{x}^{m}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(f^(c*(b*x+a)^2)*x^m,x)

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integrate(f^((b*x + a)^2*c)*x^m, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(f^((b*x + a)^2*c)*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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Sympy [A]  time = 0., size = 0, normalized size = 0. \[ \int f^{c \left (a + b x\right )^{2}} x^{m}\, dx \]

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integrate(f^((b*x + a)^2*c)*x^m, x)