3.94.25 \(\int (1-170 e^{-1-80 x^2} x) \, dx\)

Optimal. Leaf size=15 \[ \frac {17}{16} e^{-1-80 x^2}+x \]

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Rubi [A]  time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2209} \begin {gather*} \frac {17}{16} e^{-80 x^2-1}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 - 170*E^(-1 - 80*x^2)*x,x]

[Out]

(17*E^(-1 - 80*x^2))/16 + x

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} &=x-170 \int e^{-1-80 x^2} x \, dx\\ &=\frac {17}{16} e^{-1-80 x^2}+x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 15, normalized size = 1.00 \begin {gather*} \frac {17}{16} e^{-1-80 x^2}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 - 170*E^(-1 - 80*x^2)*x,x]

[Out]

(17*E^(-1 - 80*x^2))/16 + x

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fricas [A]  time = 0.60, size = 12, normalized size = 0.80 \begin {gather*} x + \frac {17}{16} \, e^{\left (-80 \, x^{2} - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-170*x*exp(-80*x^2-1)+1,x, algorithm="fricas")

[Out]

x + 17/16*e^(-80*x^2 - 1)

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giac [A]  time = 0.14, size = 12, normalized size = 0.80 \begin {gather*} x + \frac {17}{16} \, e^{\left (-80 \, x^{2} - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-170*x*exp(-80*x^2-1)+1,x, algorithm="giac")

[Out]

x + 17/16*e^(-80*x^2 - 1)

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maple [A]  time = 0.02, size = 13, normalized size = 0.87

method	result	size
default	\(x +\frac {17 \,{\mathrm e}^{-80 x^{2}-1}}{16}\)	\(13\)
norman	\(x +\frac {17 \,{\mathrm e}^{-80 x^{2}-1}}{16}\)	\(13\)
risch	\(x +\frac {17 \,{\mathrm e}^{-80 x^{2}-1}}{16}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-170*x*exp(-80*x^2-1)+1,x,method=_RETURNVERBOSE)

[Out]

x+17/16*exp(-80*x^2-1)

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maxima [A]  time = 0.37, size = 12, normalized size = 0.80 \begin {gather*} x + \frac {17}{16} \, e^{\left (-80 \, x^{2} - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-170*x*exp(-80*x^2-1)+1,x, algorithm="maxima")

[Out]

x + 17/16*e^(-80*x^2 - 1)

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mupad [B]  time = 0.12, size = 12, normalized size = 0.80 \begin {gather*} x+\frac {17\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{-80\,x^2}}{16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - 170*x*exp(- 80*x^2 - 1),x)

[Out]

x + (17*exp(-1)*exp(-80*x^2))/16

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sympy [A]  time = 0.08, size = 14, normalized size = 0.93 \begin {gather*} x + \frac {17 e^{- 80 x^{2} - 1}}{16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-170*x*exp(-80*x**2-1)+1,x)

[Out]

x + 17*exp(-80*x**2 - 1)/16

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