3.63.94 \(\int (1+e^{-10 x-5 e^{x^4} x+10 x^2} (-10+20 x+e^{x^4} (-5-20 x^4))) \, dx\)

Optimal. Leaf size=19 \[ e^{5 x \left (-2-e^{x^4}+2 x\right )}+x \]

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Rubi [A]  time = 0.15, antiderivative size = 21, normalized size of antiderivative = 1.11, number of steps used = 2, number of rules used = 1, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.025, Rules used = {6706} \begin {gather*} e^{-5 e^{x^4} x+10 x^2-10 x}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 + E^(-10*x - 5*E^x^4*x + 10*x^2)*(-10 + 20*x + E^x^4*(-5 - 20*x^4)),x]

[Out]

E^(-10*x - 5*E^x^4*x + 10*x^2) + x

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x+\int e^{-10 x-5 e^{x^4} x+10 x^2} \left (-10+20 x+e^{x^4} \left (-5-20 x^4\right )\right ) \, dx\\ &=e^{-10 x-5 e^{x^4} x+10 x^2}+x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.35, size = 21, normalized size = 1.11 \begin {gather*} e^{-10 x-5 e^{x^4} x+10 x^2}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 + E^(-10*x - 5*E^x^4*x + 10*x^2)*(-10 + 20*x + E^x^4*(-5 - 20*x^4)),x]

[Out]

E^(-10*x - 5*E^x^4*x + 10*x^2) + x

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fricas [A]  time = 0.93, size = 19, normalized size = 1.00 \begin {gather*} x + e^{\left (10 \, x^{2} - 5 \, x e^{\left (x^{4}\right )} - 10 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-20*x^4-5)*exp(x^4)+20*x-10)*exp(-5*x*exp(x^4)+10*x^2-10*x)+1,x, algorithm="fricas")

[Out]

x + e^(10*x^2 - 5*x*e^(x^4) - 10*x)

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giac [A]  time = 0.29, size = 19, normalized size = 1.00 \begin {gather*} x + e^{\left (10 \, x^{2} - 5 \, x e^{\left (x^{4}\right )} - 10 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-20*x^4-5)*exp(x^4)+20*x-10)*exp(-5*x*exp(x^4)+10*x^2-10*x)+1,x, algorithm="giac")

[Out]

x + e^(10*x^2 - 5*x*e^(x^4) - 10*x)

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maple [A]  time = 0.05, size = 18, normalized size = 0.95

method	result	size
risch	\({\mathrm e}^{5 \left (2 x -2-{\mathrm e}^{x^{4}}\right ) x}+x\)	\(18\)
default	\(x +{\mathrm e}^{-5 x \,{\mathrm e}^{x^{4}}+10 x^{2}-10 x}\)	\(20\)
norman	\(x +{\mathrm e}^{-5 x \,{\mathrm e}^{x^{4}}+10 x^{2}-10 x}\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-20*x^4-5)*exp(x^4)+20*x-10)*exp(-5*x*exp(x^4)+10*x^2-10*x)+1,x,method=_RETURNVERBOSE)

[Out]

exp(5*(2*x-2-exp(x^4))*x)+x

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maxima [A]  time = 0.44, size = 19, normalized size = 1.00 \begin {gather*} x + e^{\left (10 \, x^{2} - 5 \, x e^{\left (x^{4}\right )} - 10 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-20*x^4-5)*exp(x^4)+20*x-10)*exp(-5*x*exp(x^4)+10*x^2-10*x)+1,x, algorithm="maxima")

[Out]

x + e^(10*x^2 - 5*x*e^(x^4) - 10*x)

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mupad [B]  time = 4.12, size = 21, normalized size = 1.11 \begin {gather*} x+{\mathrm {e}}^{-10\,x}\,{\mathrm {e}}^{-5\,x\,{\mathrm {e}}^{x^4}}\,{\mathrm {e}}^{10\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - exp(10*x^2 - 5*x*exp(x^4) - 10*x)*(exp(x^4)*(20*x^4 + 5) - 20*x + 10),x)

[Out]

x + exp(-10*x)*exp(-5*x*exp(x^4))*exp(10*x^2)

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sympy [A]  time = 0.34, size = 19, normalized size = 1.00 \begin {gather*} x + e^{10 x^{2} - 5 x e^{x^{4}} - 10 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-20*x**4-5)*exp(x**4)+20*x-10)*exp(-5*x*exp(x**4)+10*x**2-10*x)+1,x)

[Out]

x + exp(10*x**2 - 5*x*exp(x**4) - 10*x)

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