3.49.50 \(\int 100 e^{-2-25 x^2} x \, dx\)

Optimal. Leaf size=15 \[ \frac {1}{e^{10}}-2 e^{-2-25 x^2} \]

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Rubi [A]  time = 0.01, antiderivative size = 11, normalized size of antiderivative = 0.73, number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 2209} \begin {gather*} -2 e^{-25 x^2-2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[100*E^(-2 - 25*x^2)*x,x]

[Out]

-2*E^(-2 - 25*x^2)

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, 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} &=100 \int e^{-2-25 x^2} x \, dx\\ &=-2 e^{-2-25 x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.73 \begin {gather*} -2 e^{-2-25 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[100*E^(-2 - 25*x^2)*x,x]

[Out]

-2*E^(-2 - 25*x^2)

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fricas [A]  time = 0.64, size = 10, normalized size = 0.67 \begin {gather*} -2 \, e^{\left (-25 \, x^{2} - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(100*x/exp(2)/exp(25*x^2),x, algorithm="fricas")

[Out]

-2*e^(-25*x^2 - 2)

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giac [A]  time = 0.16, size = 10, normalized size = 0.67 \begin {gather*} -2 \, e^{\left (-25 \, x^{2} - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(100*x/exp(2)/exp(25*x^2),x, algorithm="giac")

[Out]

-2*e^(-25*x^2 - 2)

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maple [A]  time = 0.04, size = 11, normalized size = 0.73

method	result	size
risch	\(-2 \,{\mathrm e}^{-25 x^{2}-2}\)	\(11\)
gosper	\(-2 \,{\mathrm e}^{-25 x^{2}} {\mathrm e}^{-2}\)	\(15\)
derivativedivides	\(-2 \,{\mathrm e}^{-25 x^{2}} {\mathrm e}^{-2}\)	\(15\)
default	\(-2 \,{\mathrm e}^{-25 x^{2}} {\mathrm e}^{-2}\)	\(15\)
norman	\(-2 \,{\mathrm e}^{-25 x^{2}} {\mathrm e}^{-2}\)	\(15\)
meijerg	\(2 \,{\mathrm e}^{-2} \left (1-{\mathrm e}^{-25 x^{2}}\right )\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(100*x/exp(2)/exp(25*x^2),x,method=_RETURNVERBOSE)

[Out]

-2*exp(-25*x^2-2)

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maxima [A]  time = 0.35, size = 10, normalized size = 0.67 \begin {gather*} -2 \, e^{\left (-25 \, x^{2} - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(100*x/exp(2)/exp(25*x^2),x, algorithm="maxima")

[Out]

-2*e^(-25*x^2 - 2)

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mupad [B]  time = 0.05, size = 10, normalized size = 0.67 \begin {gather*} -2\,{\mathrm {e}}^{-2}\,{\mathrm {e}}^{-25\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(100*x*exp(-2)*exp(-25*x^2),x)

[Out]

-2*exp(-2)*exp(-25*x^2)

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sympy [A]  time = 0.10, size = 12, normalized size = 0.80 \begin {gather*} - \frac {2 e^{- 25 x^{2}}}{e^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(100*x/exp(2)/exp(25*x**2),x)

[Out]

-2*exp(-2)*exp(-25*x**2)

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