3.7.60 \(\int \frac {1}{3} (11+3 e^{16+x}-6 x+9 x^2) \, dx\)

Optimal. Leaf size=21 \[ e^{16+x}-\frac {x}{3}+x \left (4-x+x^2\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 19, normalized size of antiderivative = 0.90, number of steps used = 3, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {12, 2194} \begin {gather*} x^3-x^2+\frac {11 x}{3}+e^{x+16} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(11 + 3*E^(16 + x) - 6*x + 9*x^2)/3,x]

[Out]

E^(16 + x) + (11*x)/3 - x^2 + x^3

Rule 12

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

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \left (11+3 e^{16+x}-6 x+9 x^2\right ) \, dx\\ &=\frac {11 x}{3}-x^2+x^3+\int e^{16+x} \, dx\\ &=e^{16+x}+\frac {11 x}{3}-x^2+x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 19, normalized size = 0.90 \begin {gather*} e^{16+x}+\frac {11 x}{3}-x^2+x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(11 + 3*E^(16 + x) - 6*x + 9*x^2)/3,x]

[Out]

E^(16 + x) + (11*x)/3 - x^2 + x^3

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fricas [A]  time = 0.94, size = 16, normalized size = 0.76 \begin {gather*} x^{3} - x^{2} + \frac {11}{3} \, x + e^{\left (x + 16\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x+16)+3*x^2-2*x+11/3,x, algorithm="fricas")

[Out]

x^3 - x^2 + 11/3*x + e^(x + 16)

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giac [A]  time = 0.31, size = 16, normalized size = 0.76 \begin {gather*} x^{3} - x^{2} + \frac {11}{3} \, x + e^{\left (x + 16\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x+16)+3*x^2-2*x+11/3,x, algorithm="giac")

[Out]

x^3 - x^2 + 11/3*x + e^(x + 16)

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maple [A]  time = 0.03, size = 17, normalized size = 0.81

method	result	size
default	\(\frac {11 x}{3}-x^{2}+x^{3}+{\mathrm e}^{x +16}\)	\(17\)
norman	\(\frac {11 x}{3}-x^{2}+x^{3}+{\mathrm e}^{x +16}\)	\(17\)
risch	\(\frac {11 x}{3}-x^{2}+x^{3}+{\mathrm e}^{x +16}\)	\(17\)
derivativedivides	\(\frac {107 x}{3}+\frac {1712}{3}-\left (x +16\right )^{2}+x^{3}+{\mathrm e}^{x +16}\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x+16)+3*x^2-2*x+11/3,x,method=_RETURNVERBOSE)

[Out]

11/3*x-x^2+x^3+exp(x+16)

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maxima [A]  time = 0.45, size = 16, normalized size = 0.76 \begin {gather*} x^{3} - x^{2} + \frac {11}{3} \, x + e^{\left (x + 16\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x+16)+3*x^2-2*x+11/3,x, algorithm="maxima")

[Out]

x^3 - x^2 + 11/3*x + e^(x + 16)

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mupad [B]  time = 0.06, size = 16, normalized size = 0.76 \begin {gather*} \frac {11\,x}{3}+{\mathrm {e}}^{x+16}-x^2+x^3 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x + 16) - 2*x + 3*x^2 + 11/3,x)

[Out]

(11*x)/3 + exp(x + 16) - x^2 + x^3

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sympy [A]  time = 0.09, size = 15, normalized size = 0.71 \begin {gather*} x^{3} - x^{2} + \frac {11 x}{3} + e^{x + 16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x+16)+3*x**2-2*x+11/3,x)

[Out]

x**3 - x**2 + 11*x/3 + exp(x + 16)

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