3.72.90 \(\int 2 e^{-10+e^3+e^{20 x}} (1+20 e^{20 x} x) \, dx\)

Optimal. Leaf size=15 \[ 2 e^{-10+e^3+e^{20 x}} x \]

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Rubi [A]  time = 0.02, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 2288} \begin {gather*} 2 e^{e^{20 x}-10+e^3} x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2*E^(-10 + E^3 + E^(20*x))*(1 + 20*E^(20*x)*x),x]

[Out]

2*E^(-10 + E^3 + E^(20*x))*x

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=2 \int e^{-10+e^3+e^{20 x}} \left (1+20 e^{20 x} x\right ) \, dx\\ &=2 e^{-10+e^3+e^{20 x}} x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 15, normalized size = 1.00 \begin {gather*} 2 e^{-10+e^3+e^{20 x}} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2*E^(-10 + E^3 + E^(20*x))*(1 + 20*E^(20*x)*x),x]

[Out]

2*E^(-10 + E^3 + E^(20*x))*x

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fricas [A]  time = 0.58, size = 13, normalized size = 0.87 \begin {gather*} x e^{\left (e^{3} + e^{\left (20 \, x\right )} + \log \relax (2) - 10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((20*x*exp(20*x)+1)*exp(exp(20*x)+log(2)+exp(3)-10),x, algorithm="fricas")

[Out]

x*e^(e^3 + e^(20*x) + log(2) - 10)

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giac [A]  time = 0.13, size = 12, normalized size = 0.80 \begin {gather*} 2 \, x e^{\left (e^{3} + e^{\left (20 \, x\right )} - 10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((20*x*exp(20*x)+1)*exp(exp(20*x)+log(2)+exp(3)-10),x, algorithm="giac")

[Out]

2*x*e^(e^3 + e^(20*x) - 10)

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maple [A]  time = 0.04, size = 13, normalized size = 0.87

method	result	size
risch	\(2 \,{\mathrm e}^{{\mathrm e}^{20 x}-10+{\mathrm e}^{3}} x\)	\(13\)
norman	\({\mathrm e}^{{\mathrm e}^{20 x}+\ln \relax (2)+{\mathrm e}^{3}-10} x\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((20*x*exp(20*x)+1)*exp(exp(20*x)+ln(2)+exp(3)-10),x,method=_RETURNVERBOSE)

[Out]

2*exp(exp(20*x)-10+exp(3))*x

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} 2 \, x e^{\left (e^{3} + e^{\left (20 \, x\right )} - 10\right )} + \frac {1}{10} \, {\rm Ei}\left (e^{\left (20 \, x\right )}\right ) e^{\left (e^{3} - 10\right )} - 2 \, \int e^{\left (e^{3} + e^{\left (20 \, x\right )} - 10\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((20*x*exp(20*x)+1)*exp(exp(20*x)+log(2)+exp(3)-10),x, algorithm="maxima")

[Out]

2*x*e^(e^3 + e^(20*x) - 10) + 1/10*Ei(e^(20*x))*e^(e^3 - 10) - 2*integrate(e^(e^3 + e^(20*x) - 10), x)

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mupad [B]  time = 0.06, size = 13, normalized size = 0.87 \begin {gather*} 2\,x\,{\mathrm {e}}^{-10}\,{\mathrm {e}}^{{\mathrm {e}}^{20\,x}}\,{\mathrm {e}}^{{\mathrm {e}}^3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(exp(20*x) + exp(3) + log(2) - 10)*(20*x*exp(20*x) + 1),x)

[Out]

2*x*exp(-10)*exp(exp(20*x))*exp(exp(3))

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sympy [A]  time = 0.17, size = 14, normalized size = 0.93 \begin {gather*} 2 x e^{e^{20 x} - 10 + e^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((20*x*exp(20*x)+1)*exp(exp(20*x)+ln(2)+exp(3)-10),x)

[Out]

2*x*exp(exp(20*x) - 10 + exp(3))

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