3.64.9 \(\int (3+3 e^x+16 x+4 x^3) \, dx\)

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

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Rubi [A]  time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.06, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2194} \begin {gather*} x^4+8 x^2+3 x+3 e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3 + 3*E^x + 16*x + 4*x^3,x]

[Out]

3*E^x + 3*x + 8*x^2 + x^4

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} &=3 x+8 x^2+x^4+3 \int e^x \, dx\\ &=3 e^x+3 x+8 x^2+x^4\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 17, normalized size = 1.06 \begin {gather*} 3 e^x+3 x+8 x^2+x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3 + 3*E^x + 16*x + 4*x^3,x]

[Out]

3*E^x + 3*x + 8*x^2 + x^4

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fricas [A]  time = 0.68, size = 16, normalized size = 1.00 \begin {gather*} x^{4} + 8 \, x^{2} + 3 \, x + 3 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(x)+4*x^3+16*x+3,x, algorithm="fricas")

[Out]

x^4 + 8*x^2 + 3*x + 3*e^x

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giac [A]  time = 0.13, size = 16, normalized size = 1.00 \begin {gather*} x^{4} + 8 \, x^{2} + 3 \, x + 3 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(x)+4*x^3+16*x+3,x, algorithm="giac")

[Out]

x^4 + 8*x^2 + 3*x + 3*e^x

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maple [A]  time = 0.03, size = 17, normalized size = 1.06

method	result	size
default	\(x^{4}+8 x^{2}+3 x +3 \,{\mathrm e}^{x}\)	\(17\)
norman	\(x^{4}+8 x^{2}+3 x +3 \,{\mathrm e}^{x}\)	\(17\)
risch	\(x^{4}+8 x^{2}+3 x +3 \,{\mathrm e}^{x}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*exp(x)+4*x^3+16*x+3,x,method=_RETURNVERBOSE)

[Out]

x^4+8*x^2+3*x+3*exp(x)

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maxima [A]  time = 0.37, size = 16, normalized size = 1.00 \begin {gather*} x^{4} + 8 \, x^{2} + 3 \, x + 3 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(x)+4*x^3+16*x+3,x, algorithm="maxima")

[Out]

x^4 + 8*x^2 + 3*x + 3*e^x

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mupad [B]  time = 4.17, size = 16, normalized size = 1.00 \begin {gather*} 3\,x+3\,{\mathrm {e}}^x+8\,x^2+x^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(16*x + 3*exp(x) + 4*x^3 + 3,x)

[Out]

3*x + 3*exp(x) + 8*x^2 + x^4

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sympy [A]  time = 0.08, size = 15, normalized size = 0.94 \begin {gather*} x^{4} + 8 x^{2} + 3 x + 3 e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(x)+4*x**3+16*x+3,x)

[Out]

x**4 + 8*x**2 + 3*x + 3*exp(x)

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