3.3.41 \(\int f^{c (a+b x)^2} x^m \, dx\) [241]

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

[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 = 0.04, 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 = {} \begin {gather*} \int f^{c (a+b x)^2} x^m \, dx \end {gather*}

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 = 0.12, size = 0, normalized size = 0.00 \begin {gather*} \int f^{c (a+b x)^2} x^m \, dx \end {gather*}

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 = 0.01, size = 0, normalized size = 0.00 \[\int f^{c \left (b x +a \right )^{2}} x^{m}\, dx\]

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

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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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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

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 [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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

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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