3.78.14 \(\int (-22+e^x-2 x+18 x^2-4 x^3) \, dx\)

Optimal. Leaf size=21 \[ e^x-\left (-5+(-1+x)^2-x\right )^2+2 x \]

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Rubi [A]  time = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.05, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2194} \begin {gather*} -x^4+6 x^3-x^2-22 x+e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-22 + E^x - 2*x + 18*x^2 - 4*x^3,x]

[Out]

E^x - 22*x - x^2 + 6*x^3 - 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} &=-22 x-x^2+6 x^3-x^4+\int e^x \, dx\\ &=e^x-22 x-x^2+6 x^3-x^4\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 22, normalized size = 1.05 \begin {gather*} e^x-22 x-x^2+6 x^3-x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-22 + E^x - 2*x + 18*x^2 - 4*x^3,x]

[Out]

E^x - 22*x - x^2 + 6*x^3 - x^4

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fricas [A]  time = 0.60, size = 21, normalized size = 1.00 \begin {gather*} -x^{4} + 6 \, x^{3} - x^{2} - 22 \, x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)-4*x^3+18*x^2-2*x-22,x, algorithm="fricas")

[Out]

-x^4 + 6*x^3 - x^2 - 22*x + e^x

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giac [A]  time = 0.14, size = 21, normalized size = 1.00 \begin {gather*} -x^{4} + 6 \, x^{3} - x^{2} - 22 \, x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)-4*x^3+18*x^2-2*x-22,x, algorithm="giac")

[Out]

-x^4 + 6*x^3 - x^2 - 22*x + e^x

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maple [A]  time = 0.01, size = 22, normalized size = 1.05

method	result	size
default	\(-x^{4}+6 x^{3}-x^{2}-22 x +{\mathrm e}^{x}\)	\(22\)
norman	\(-x^{4}+6 x^{3}-x^{2}-22 x +{\mathrm e}^{x}\)	\(22\)
risch	\(-x^{4}+6 x^{3}-x^{2}-22 x +{\mathrm e}^{x}\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x)-4*x^3+18*x^2-2*x-22,x,method=_RETURNVERBOSE)

[Out]

-x^4+6*x^3-x^2-22*x+exp(x)

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maxima [A]  time = 0.35, size = 21, normalized size = 1.00 \begin {gather*} -x^{4} + 6 \, x^{3} - x^{2} - 22 \, x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)-4*x^3+18*x^2-2*x-22,x, algorithm="maxima")

[Out]

-x^4 + 6*x^3 - x^2 - 22*x + e^x

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mupad [B]  time = 0.06, size = 21, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^x-22\,x-x^2+6\,x^3-x^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x) - 2*x + 18*x^2 - 4*x^3 - 22,x)

[Out]

exp(x) - 22*x - x^2 + 6*x^3 - x^4

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sympy [A]  time = 0.08, size = 17, normalized size = 0.81 \begin {gather*} - x^{4} + 6 x^{3} - x^{2} - 22 x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)-4*x**3+18*x**2-2*x-22,x)

[Out]

-x**4 + 6*x**3 - x**2 - 22*x + exp(x)

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