\(\int (12+18 x+e^{25-11 x+x^2} (-11+2 x)) \, dx\) [1218]

Optimal result

Integrand size = 21, antiderivative size = 28 \[ \int \left (12+18 x+e^{25-11 x+x^2} (-11+2 x)\right ) \, dx=4-e^3+e^{(-5+x)^2-x}+3 x+9 \left (x+x^2\right ) \]

[Out]

4+12*x+9*x^2-exp(3)+exp((-5+x)^2-x)

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.68, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {2268} \[ \int \left (12+18 x+e^{25-11 x+x^2} (-11+2 x)\right ) \, dx=9 x^2+e^{x^2-11 x+25}+12 x \]

[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 2268

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{align*} \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{align*}

Mathematica [A] (verified)

Time = 0.04 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.68 \[ \int \left (12+18 x+e^{25-11 x+x^2} (-11+2 x)\right ) \, dx=e^{25-11 x+x^2}+12 x+9 x^2 \]

[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

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 19, normalized size of antiderivative = 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	\(12 x +{\mathrm e}^{x^{2}-11 x +25}+9 x^{2}\)	\(19\)
parallelrisch	\(12 x +{\mathrm e}^{x^{2}-11 x +25}+9 x^{2}\)	\(19\)
parts	\(12 x +{\mathrm e}^{x^{2}-11 x +25}+9 x^{2}\)	\(19\)

[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

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.64 \[ \int \left (12+18 x+e^{25-11 x+x^2} (-11+2 x)\right ) \, dx=9 \, x^{2} + 12 \, x + e^{\left (x^{2} - 11 \, x + 25\right )} \]

[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)

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.61 \[ \int \left (12+18 x+e^{25-11 x+x^2} (-11+2 x)\right ) \, dx=9 x^{2} + 12 x + e^{x^{2} - 11 x + 25} \]

[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)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.64 \[ \int \left (12+18 x+e^{25-11 x+x^2} (-11+2 x)\right ) \, dx=9 \, x^{2} + 12 \, x + e^{\left (x^{2} - 11 \, x + 25\right )} \]

[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)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.64 \[ \int \left (12+18 x+e^{25-11 x+x^2} (-11+2 x)\right ) \, dx=9 \, x^{2} + 12 \, x + e^{\left (x^{2} - 11 \, x + 25\right )} \]

[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)

Mupad [B] (verification not implemented)

Time = 7.89 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.71 \[ \int \left (12+18 x+e^{25-11 x+x^2} (-11+2 x)\right ) \, dx=12\,x+9\,x^2+{\mathrm {e}}^{-11\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{25} \]

[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)