3.6.47 \(\int e^{8-117 x+15 x^2} (-117+30 x) \, dx\)

Optimal. Leaf size=18 \[ e^{8+x (3-x+8 (-15+2 x))} \]

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Rubi [A]  time = 0.01, antiderivative size = 12, normalized size of antiderivative = 0.67, number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2236} \begin {gather*} e^{15 x^2-117 x+8} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(8 - 117*x + 15*x^2)*(-117 + 30*x),x]

[Out]

E^(8 - 117*x + 15*x^2)

Rule 2236

Int[(F_)^((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)*((d_.) + (e_.)*(x_)), x_Symbol] :> Simp[(e*F^(a + b*x + c*x^2))/(
2*c*Log[F]), x] /; FreeQ[{F, a, b, c, d, e}, x] && EqQ[b*e - 2*c*d, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=e^{8-117 x+15 x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.03, size = 12, normalized size = 0.67 \begin {gather*} e^{8-117 x+15 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(8 - 117*x + 15*x^2)*(-117 + 30*x),x]

[Out]

E^(8 - 117*x + 15*x^2)

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fricas [A]  time = 0.74, size = 11, normalized size = 0.61 \begin {gather*} e^{\left (15 \, x^{2} - 117 \, x + 8\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((30*x-117)*exp(15*x^2-117*x+8),x, algorithm="fricas")

[Out]

e^(15*x^2 - 117*x + 8)

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giac [A]  time = 0.25, size = 11, normalized size = 0.61 \begin {gather*} e^{\left (15 \, x^{2} - 117 \, x + 8\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((30*x-117)*exp(15*x^2-117*x+8),x, algorithm="giac")

[Out]

e^(15*x^2 - 117*x + 8)

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maple [A]  time = 0.05, size = 12, normalized size = 0.67

method	result	size
gosper	\({\mathrm e}^{15 x^{2}-117 x +8}\)	\(12\)
derivativedivides	\({\mathrm e}^{15 x^{2}-117 x +8}\)	\(12\)
default	\({\mathrm e}^{15 x^{2}-117 x +8}\)	\(12\)
norman	\({\mathrm e}^{15 x^{2}-117 x +8}\)	\(12\)
risch	\({\mathrm e}^{15 x^{2}-117 x +8}\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((30*x-117)*exp(15*x^2-117*x+8),x,method=_RETURNVERBOSE)

[Out]

exp(15*x^2-117*x+8)

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maxima [A]  time = 0.42, size = 11, normalized size = 0.61 \begin {gather*} e^{\left (15 \, x^{2} - 117 \, x + 8\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((30*x-117)*exp(15*x^2-117*x+8),x, algorithm="maxima")

[Out]

e^(15*x^2 - 117*x + 8)

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mupad [B]  time = 0.07, size = 13, normalized size = 0.72 \begin {gather*} {\mathrm {e}}^{-117\,x}\,{\mathrm {e}}^8\,{\mathrm {e}}^{15\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(15*x^2 - 117*x + 8)*(30*x - 117),x)

[Out]

exp(-117*x)*exp(8)*exp(15*x^2)

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sympy [A]  time = 0.09, size = 10, normalized size = 0.56 \begin {gather*} e^{15 x^{2} - 117 x + 8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((30*x-117)*exp(15*x**2-117*x+8),x)

[Out]

exp(15*x**2 - 117*x + 8)

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