3.72.28 \(\int \frac {1}{4} (4+e^{\frac {1}{4} (-554725+149161 x-6371 x^2-529 x^3)} (149161-12742 x-1587 x^2)) \, dx\)

Optimal. Leaf size=29 \[ e^{(25+x) \left (3-\left (12 (6-x)+\frac {5+x}{2}\right )^2\right )}+x \]

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Rubi [A]  time = 0.07, antiderivative size = 23, normalized size of antiderivative = 0.79, number of steps used = 3, number of rules used = 2, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {12, 6706} \begin {gather*} e^{\frac {1}{4} \left (-529 x^3-6371 x^2+149161 x-554725\right )}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(4 + E^((-554725 + 149161*x - 6371*x^2 - 529*x^3)/4)*(149161 - 12742*x - 1587*x^2))/4,x]

[Out]

E^((-554725 + 149161*x - 6371*x^2 - 529*x^3)/4) + 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 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} &=\frac {1}{4} \int \left (4+e^{\frac {1}{4} \left (-554725+149161 x-6371 x^2-529 x^3\right )} \left (149161-12742 x-1587 x^2\right )\right ) \, dx\\ &=x+\frac {1}{4} \int e^{\frac {1}{4} \left (-554725+149161 x-6371 x^2-529 x^3\right )} \left (149161-12742 x-1587 x^2\right ) \, dx\\ &=e^{\frac {1}{4} \left (-554725+149161 x-6371 x^2-529 x^3\right )}+x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.38, size = 27, normalized size = 0.93 \begin {gather*} e^{-\frac {554725}{4}+\frac {149161 x}{4}-\frac {6371 x^2}{4}-\frac {529 x^3}{4}}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4 + E^((-554725 + 149161*x - 6371*x^2 - 529*x^3)/4)*(149161 - 12742*x - 1587*x^2))/4,x]

[Out]

E^(-554725/4 + (149161*x)/4 - (6371*x^2)/4 - (529*x^3)/4) + x

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fricas [A]  time = 0.94, size = 18, normalized size = 0.62 \begin {gather*} x + e^{\left (-\frac {529}{4} \, x^{3} - \frac {6371}{4} \, x^{2} + \frac {149161}{4} \, x - \frac {554725}{4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(-1587*x^2-12742*x+149161)*exp(-529/4*x^3-6371/4*x^2+149161/4*x-554725/4)+1,x, algorithm="fricas
")

[Out]

x + e^(-529/4*x^3 - 6371/4*x^2 + 149161/4*x - 554725/4)

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giac [A]  time = 0.15, size = 18, normalized size = 0.62 \begin {gather*} x + e^{\left (-\frac {529}{4} \, x^{3} - \frac {6371}{4} \, x^{2} + \frac {149161}{4} \, x - \frac {554725}{4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(-1587*x^2-12742*x+149161)*exp(-529/4*x^3-6371/4*x^2+149161/4*x-554725/4)+1,x, algorithm="giac")

[Out]

x + e^(-529/4*x^3 - 6371/4*x^2 + 149161/4*x - 554725/4)

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maple [A]  time = 0.05, size = 19, normalized size = 0.66

method	result	size
default	\(x +{\mathrm e}^{-\frac {529}{4} x^{3}-\frac {6371}{4} x^{2}+\frac {149161}{4} x -\frac {554725}{4}}\)	\(19\)
norman	\(x +{\mathrm e}^{-\frac {529}{4} x^{3}-\frac {6371}{4} x^{2}+\frac {149161}{4} x -\frac {554725}{4}}\)	\(19\)
risch	\(x +{\mathrm e}^{-\frac {\left (x +25\right ) \left (529 x^{2}-6854 x +22189\right )}{4}}\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/4*(-1587*x^2-12742*x+149161)*exp(-529/4*x^3-6371/4*x^2+149161/4*x-554725/4)+1,x,method=_RETURNVERBOSE)

[Out]

x+exp(-529/4*x^3-6371/4*x^2+149161/4*x-554725/4)

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maxima [A]  time = 0.35, size = 18, normalized size = 0.62 \begin {gather*} x + e^{\left (-\frac {529}{4} \, x^{3} - \frac {6371}{4} \, x^{2} + \frac {149161}{4} \, x - \frac {554725}{4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(-1587*x^2-12742*x+149161)*exp(-529/4*x^3-6371/4*x^2+149161/4*x-554725/4)+1,x, algorithm="maxima
")

[Out]

x + e^(-529/4*x^3 - 6371/4*x^2 + 149161/4*x - 554725/4)

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mupad [B]  time = 0.09, size = 18, normalized size = 0.62 \begin {gather*} x+{\mathrm {e}}^{-\frac {529\,x^3}{4}-\frac {6371\,x^2}{4}+\frac {149161\,x}{4}-\frac {554725}{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - (exp((149161*x)/4 - (6371*x^2)/4 - (529*x^3)/4 - 554725/4)*(12742*x + 1587*x^2 - 149161))/4,x)

[Out]

x + exp((149161*x)/4 - (6371*x^2)/4 - (529*x^3)/4 - 554725/4)

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sympy [A]  time = 0.13, size = 24, normalized size = 0.83 \begin {gather*} x + e^{- \frac {529 x^{3}}{4} - \frac {6371 x^{2}}{4} + \frac {149161 x}{4} - \frac {554725}{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(-1587*x**2-12742*x+149161)*exp(-529/4*x**3-6371/4*x**2+149161/4*x-554725/4)+1,x)

[Out]

x + exp(-529*x**3/4 - 6371*x**2/4 + 149161*x/4 - 554725/4)

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