3.102.8 \(\int (5-2 x-2 e^{x^2} x) \, dx\)

Optimal. Leaf size=20 \[ 4+e^6-e^{x^2}+x+(4-x) x \]

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.80, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2209} \begin {gather*} -x^2-e^{x^2}+5 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[5 - 2*x - 2*E^x^2*x,x]

[Out]

-E^x^2 + 5*x - x^2

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=5 x-x^2-2 \int e^{x^2} x \, dx\\ &=-e^{x^2}+5 x-x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 16, normalized size = 0.80 \begin {gather*} -e^{x^2}+5 x-x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[5 - 2*x - 2*E^x^2*x,x]

[Out]

-E^x^2 + 5*x - x^2

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fricas [A]  time = 0.45, size = 15, normalized size = 0.75 \begin {gather*} -x^{2} + 5 \, x - e^{\left (x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(x^2)*x-2*x+5,x, algorithm="fricas")

[Out]

-x^2 + 5*x - e^(x^2)

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giac [A]  time = 0.12, size = 15, normalized size = 0.75 \begin {gather*} -x^{2} + 5 \, x - e^{\left (x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(x^2)*x-2*x+5,x, algorithm="giac")

[Out]

-x^2 + 5*x - e^(x^2)

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maple [A]  time = 0.01, size = 16, normalized size = 0.80

method	result	size
default	\(-x^{2}+5 x -{\mathrm e}^{x^{2}}\)	\(16\)
norman	\(-x^{2}+5 x -{\mathrm e}^{x^{2}}\)	\(16\)
risch	\(-x^{2}+5 x -{\mathrm e}^{x^{2}}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2*exp(x^2)*x-2*x+5,x,method=_RETURNVERBOSE)

[Out]

-x^2+5*x-exp(x^2)

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maxima [A]  time = 0.35, size = 15, normalized size = 0.75 \begin {gather*} -x^{2} + 5 \, x - e^{\left (x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(x^2)*x-2*x+5,x, algorithm="maxima")

[Out]

-x^2 + 5*x - e^(x^2)

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mupad [B]  time = 0.07, size = 15, normalized size = 0.75 \begin {gather*} 5\,x-{\mathrm {e}}^{x^2}-x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5 - 2*x*exp(x^2) - 2*x,x)

[Out]

5*x - exp(x^2) - x^2

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sympy [A]  time = 0.09, size = 10, normalized size = 0.50 \begin {gather*} - x^{2} + 5 x - e^{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(x**2)*x-2*x+5,x)

[Out]

-x**2 + 5*x - exp(x**2)

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