3.61.33 \(\int e^{12+16 x+7 x^2+x^3} (64+56 x+12 x^2) \, dx\)

Optimal. Leaf size=15 \[ -36+4 e^{(2+x)^2 (3+x)} \]

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Rubi [A]  time = 0.04, antiderivative size = 17, normalized size of antiderivative = 1.13, number of steps used = 1, number of rules used = 1, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {6706} \begin {gather*} 4 e^{x^3+7 x^2+16 x+12} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(12 + 16*x + 7*x^2 + x^3)*(64 + 56*x + 12*x^2),x]

[Out]

4*E^(12 + 16*x + 7*x^2 + x^3)

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} &=4 e^{12+16 x+7 x^2+x^3}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.08, size = 15, normalized size = 1.00 \begin {gather*} 4 e^{(2+x)^2+(2+x)^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(12 + 16*x + 7*x^2 + x^3)*(64 + 56*x + 12*x^2),x]

[Out]

4*E^((2 + x)^2 + (2 + x)^3)

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fricas [A]  time = 0.61, size = 16, normalized size = 1.07 \begin {gather*} 4 \, e^{\left (x^{3} + 7 \, x^{2} + 16 \, x + 12\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((12*x^2+56*x+64)*exp(x^3+7*x^2+16*x+12),x, algorithm="fricas")

[Out]

4*e^(x^3 + 7*x^2 + 16*x + 12)

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giac [A]  time = 0.22, size = 16, normalized size = 1.07 \begin {gather*} 4 \, e^{\left (x^{3} + 7 \, x^{2} + 16 \, x + 12\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((12*x^2+56*x+64)*exp(x^3+7*x^2+16*x+12),x, algorithm="giac")

[Out]

4*e^(x^3 + 7*x^2 + 16*x + 12)

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maple [A]  time = 0.02, size = 13, normalized size = 0.87

method	result	size
risch	\(4 \,{\mathrm e}^{\left (3+x \right ) \left (2+x \right )^{2}}\)	\(13\)
gosper	\(4 \,{\mathrm e}^{x^{3}+7 x^{2}+16 x +12}\)	\(17\)
default	\(4 \,{\mathrm e}^{x^{3}+7 x^{2}+16 x +12}\)	\(17\)
norman	\(4 \,{\mathrm e}^{x^{3}+7 x^{2}+16 x +12}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((12*x^2+56*x+64)*exp(x^3+7*x^2+16*x+12),x,method=_RETURNVERBOSE)

[Out]

4*exp((3+x)*(2+x)^2)

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maxima [A]  time = 0.35, size = 16, normalized size = 1.07 \begin {gather*} 4 \, e^{\left (x^{3} + 7 \, x^{2} + 16 \, x + 12\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((12*x^2+56*x+64)*exp(x^3+7*x^2+16*x+12),x, algorithm="maxima")

[Out]

4*e^(x^3 + 7*x^2 + 16*x + 12)

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mupad [B]  time = 0.05, size = 18, normalized size = 1.20 \begin {gather*} 4\,{\mathrm {e}}^{16\,x}\,{\mathrm {e}}^{x^3}\,{\mathrm {e}}^{12}\,{\mathrm {e}}^{7\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(16*x + 7*x^2 + x^3 + 12)*(56*x + 12*x^2 + 64),x)

[Out]

4*exp(16*x)*exp(x^3)*exp(12)*exp(7*x^2)

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sympy [A]  time = 0.11, size = 15, normalized size = 1.00 \begin {gather*} 4 e^{x^{3} + 7 x^{2} + 16 x + 12} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((12*x**2+56*x+64)*exp(x**3+7*x**2+16*x+12),x)

[Out]

4*exp(x**3 + 7*x**2 + 16*x + 12)

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