3.13.18 \(\int (12+18 x+e^{25-11 x+x^2} (-11+2 x)) \, dx\)

Optimal. Leaf size=28 \[ 4-e^3+e^{(-5+x)^2-x}+3 x+9 \left (x+x^2\right ) \]

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Rubi [A]  time = 0.02, antiderivative size = 19, normalized size of antiderivative = 0.68, number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {2236} \begin {gather*} 9 x^2+e^{x^2-11 x+25}+12 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[12 + 18*x + E^(25 - 11*x + x^2)*(-11 + 2*x),x]

[Out]

E^(25 - 11*x + x^2) + 12*x + 9*x^2

Rule 2236

Int[(F_)^((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)*((d_.) + (e_.)*(x_)), x_Symbol] :> Simp[(e*F^(a + b*x + c*x^2))/(
2*c*Log[F]), x] /; FreeQ[{F, a, b, c, d, e}, x] && EqQ[b*e - 2*c*d, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=12 x+9 x^2+\int e^{25-11 x+x^2} (-11+2 x) \, dx\\ &=e^{25-11 x+x^2}+12 x+9 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.04, size = 19, normalized size = 0.68 \begin {gather*} e^{25-11 x+x^2}+12 x+9 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[12 + 18*x + E^(25 - 11*x + x^2)*(-11 + 2*x),x]

[Out]

E^(25 - 11*x + x^2) + 12*x + 9*x^2

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fricas [A]  time = 0.59, size = 18, normalized size = 0.64 \begin {gather*} 9 \, x^{2} + 12 \, x + e^{\left (x^{2} - 11 \, x + 25\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x-11)*exp(x^2-11*x+25)+18*x+12,x, algorithm="fricas")

[Out]

9*x^2 + 12*x + e^(x^2 - 11*x + 25)

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giac [A]  time = 0.37, size = 18, normalized size = 0.64 \begin {gather*} 9 \, x^{2} + 12 \, x + e^{\left (x^{2} - 11 \, x + 25\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x-11)*exp(x^2-11*x+25)+18*x+12,x, algorithm="giac")

[Out]

9*x^2 + 12*x + e^(x^2 - 11*x + 25)

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maple [A]  time = 0.02, size = 19, normalized size = 0.68

method	result	size
default	\(12 x +{\mathrm e}^{x^{2}-11 x +25}+9 x^{2}\)	\(19\)
norman	\(12 x +{\mathrm e}^{x^{2}-11 x +25}+9 x^{2}\)	\(19\)
risch	\(12 x +{\mathrm e}^{x^{2}-11 x +25}+9 x^{2}\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x-11)*exp(x^2-11*x+25)+18*x+12,x,method=_RETURNVERBOSE)

[Out]

12*x+exp(x^2-11*x+25)+9*x^2

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maxima [A]  time = 0.41, size = 18, normalized size = 0.64 \begin {gather*} 9 \, x^{2} + 12 \, x + e^{\left (x^{2} - 11 \, x + 25\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x-11)*exp(x^2-11*x+25)+18*x+12,x, algorithm="maxima")

[Out]

9*x^2 + 12*x + e^(x^2 - 11*x + 25)

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mupad [B]  time = 0.08, size = 20, normalized size = 0.71 \begin {gather*} 12\,x+9\,x^2+{\mathrm {e}}^{-11\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(18*x + exp(x^2 - 11*x + 25)*(2*x - 11) + 12,x)

[Out]

12*x + 9*x^2 + exp(-11*x)*exp(x^2)*exp(25)

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sympy [A]  time = 0.09, size = 17, normalized size = 0.61 \begin {gather*} 9 x^{2} + 12 x + e^{x^{2} - 11 x + 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x-11)*exp(x**2-11*x+25)+18*x+12,x)

[Out]

9*x**2 + 12*x + exp(x**2 - 11*x + 25)

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