3.13.81 \(\int (-3+e^x+2 x) \, dx\)

Optimal. Leaf size=19 \[ -2+e^2-e^{16}+e^x-3 x+x^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.53, number of steps used = 2, number of rules used = 1, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2194} \begin {gather*} x^2-3 x+e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-3 + E^x + 2*x,x]

[Out]

E^x - 3*x + x^2

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

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.53 \begin {gather*} e^x-3 x+x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-3 + E^x + 2*x,x]

[Out]

E^x - 3*x + x^2

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fricas [A]  time = 0.62, size = 9, normalized size = 0.47 \begin {gather*} x^{2} - 3 \, x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+2*x-3,x, algorithm="fricas")

[Out]

x^2 - 3*x + e^x

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giac [A]  time = 0.20, size = 9, normalized size = 0.47 \begin {gather*} x^{2} - 3 \, x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+2*x-3,x, algorithm="giac")

[Out]

x^2 - 3*x + e^x

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maple [A]  time = 0.01, size = 10, normalized size = 0.53

method	result	size
default	\({\mathrm e}^{x}+x^{2}-3 x\)	\(10\)
norman	\({\mathrm e}^{x}+x^{2}-3 x\)	\(10\)
risch	\({\mathrm e}^{x}+x^{2}-3 x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x)+2*x-3,x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.41, size = 9, normalized size = 0.47 \begin {gather*} x^{2} - 3 \, x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+2*x-3,x, algorithm="maxima")

[Out]

x^2 - 3*x + e^x

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mupad [B]  time = 0.04, size = 9, normalized size = 0.47 \begin {gather*} {\mathrm {e}}^x-3\,x+x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + exp(x) - 3,x)

[Out]

exp(x) - 3*x + x^2

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sympy [A]  time = 0.07, size = 8, normalized size = 0.42 \begin {gather*} x^{2} - 3 x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+2*x-3,x)

[Out]

x**2 - 3*x + exp(x)

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