3.52.87 \(\int (-1+e^x+e^3 (-46 x+3 x^2)) \, dx\)

Optimal. Leaf size=20 \[ e^x-x-e^3 (23-x) x^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.10, number of steps used = 3, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2194} \begin {gather*} e^3 x^3-23 e^3 x^2-x+e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 + E^x + E^3*(-46*x + 3*x^2),x]

[Out]

E^x - x - 23*E^3*x^2 + E^3*x^3

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} &=-x+e^3 \int \left (-46 x+3 x^2\right ) \, dx+\int e^x \, dx\\ &=e^x-x-23 e^3 x^2+e^3 x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 22, normalized size = 1.10 \begin {gather*} e^x-x-23 e^3 x^2+e^3 x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 + E^x + E^3*(-46*x + 3*x^2),x]

[Out]

E^x - x - 23*E^3*x^2 + E^3*x^3

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fricas [A]  time = 0.45, size = 18, normalized size = 0.90 \begin {gather*} {\left (x^{3} - 23 \, x^{2}\right )} e^{3} - x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+(3*x^2-46*x)*exp(3)-1,x, algorithm="fricas")

[Out]

(x^3 - 23*x^2)*e^3 - x + e^x

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giac [A]  time = 0.20, size = 18, normalized size = 0.90 \begin {gather*} {\left (x^{3} - 23 \, x^{2}\right )} e^{3} - x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+(3*x^2-46*x)*exp(3)-1,x, algorithm="giac")

[Out]

(x^3 - 23*x^2)*e^3 - x + e^x

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maple [A]  time = 0.03, size = 19, normalized size = 0.95

method	result	size
default	\(-x +{\mathrm e}^{3} \left (x^{3}-23 x^{2}\right )+{\mathrm e}^{x}\)	\(19\)
norman	\(x^{3} {\mathrm e}^{3}-x -23 x^{2} {\mathrm e}^{3}+{\mathrm e}^{x}\)	\(20\)
risch	\(x^{3} {\mathrm e}^{3}-x -23 x^{2} {\mathrm e}^{3}+{\mathrm e}^{x}\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x)+(3*x^2-46*x)*exp(3)-1,x,method=_RETURNVERBOSE)

[Out]

-x+exp(3)*(x^3-23*x^2)+exp(x)

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maxima [A]  time = 0.34, size = 18, normalized size = 0.90 \begin {gather*} {\left (x^{3} - 23 \, x^{2}\right )} e^{3} - x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+(3*x^2-46*x)*exp(3)-1,x, algorithm="maxima")

[Out]

(x^3 - 23*x^2)*e^3 - x + e^x

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mupad [B]  time = 0.06, size = 19, normalized size = 0.95 \begin {gather*} {\mathrm {e}}^x-x-23\,x^2\,{\mathrm {e}}^3+x^3\,{\mathrm {e}}^3 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x) - exp(3)*(46*x - 3*x^2) - 1,x)

[Out]

exp(x) - x - 23*x^2*exp(3) + x^3*exp(3)

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sympy [A]  time = 0.08, size = 19, normalized size = 0.95 \begin {gather*} x^{3} e^{3} - 23 x^{2} e^{3} - x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+(3*x**2-46*x)*exp(3)-1,x)

[Out]

x**3*exp(3) - 23*x**2*exp(3) - x + exp(x)

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