3.81.1 \(\int (-60-e^x+178 x-72 x^2+64 x^3) \, dx\)

Optimal. Leaf size=21 \[ -e^x+\left (6+x+4 \left (1-x+x^2\right )\right )^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 24, normalized size of antiderivative = 1.14, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {2194} \begin {gather*} 16 x^4-24 x^3+89 x^2-60 x-e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-60 - E^x + 178*x - 72*x^2 + 64*x^3,x]

[Out]

-E^x - 60*x + 89*x^2 - 24*x^3 + 16*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} &=-60 x+89 x^2-24 x^3+16 x^4-\int e^x \, dx\\ &=-e^x-60 x+89 x^2-24 x^3+16 x^4\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 24, normalized size = 1.14 \begin {gather*} -e^x-60 x+89 x^2-24 x^3+16 x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-60 - E^x + 178*x - 72*x^2 + 64*x^3,x]

[Out]

-E^x - 60*x + 89*x^2 - 24*x^3 + 16*x^4

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fricas [A]  time = 0.62, size = 23, normalized size = 1.10 \begin {gather*} 16 \, x^{4} - 24 \, x^{3} + 89 \, x^{2} - 60 \, x - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(x)+64*x^3-72*x^2+178*x-60,x, algorithm="fricas")

[Out]

16*x^4 - 24*x^3 + 89*x^2 - 60*x - e^x

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giac [A]  time = 0.21, size = 23, normalized size = 1.10 \begin {gather*} 16 \, x^{4} - 24 \, x^{3} + 89 \, x^{2} - 60 \, x - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(x)+64*x^3-72*x^2+178*x-60,x, algorithm="giac")

[Out]

16*x^4 - 24*x^3 + 89*x^2 - 60*x - e^x

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maple [A]  time = 0.02, size = 24, normalized size = 1.14

method	result	size
default	\(16 x^{4}-24 x^{3}+89 x^{2}-60 x -{\mathrm e}^{x}\)	\(24\)
norman	\(16 x^{4}-24 x^{3}+89 x^{2}-60 x -{\mathrm e}^{x}\)	\(24\)
risch	\(16 x^{4}-24 x^{3}+89 x^{2}-60 x -{\mathrm e}^{x}\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(x)+64*x^3-72*x^2+178*x-60,x,method=_RETURNVERBOSE)

[Out]

16*x^4-24*x^3+89*x^2-60*x-exp(x)

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maxima [A]  time = 0.36, size = 23, normalized size = 1.10 \begin {gather*} 16 \, x^{4} - 24 \, x^{3} + 89 \, x^{2} - 60 \, x - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(x)+64*x^3-72*x^2+178*x-60,x, algorithm="maxima")

[Out]

16*x^4 - 24*x^3 + 89*x^2 - 60*x - e^x

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mupad [B]  time = 0.05, size = 23, normalized size = 1.10 \begin {gather*} 89\,x^2-{\mathrm {e}}^x-60\,x-24\,x^3+16\,x^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(178*x - exp(x) - 72*x^2 + 64*x^3 - 60,x)

[Out]

89*x^2 - exp(x) - 60*x - 24*x^3 + 16*x^4

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sympy [A]  time = 0.08, size = 20, normalized size = 0.95 \begin {gather*} 16 x^{4} - 24 x^{3} + 89 x^{2} - 60 x - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(x)+64*x**3-72*x**2+178*x-60,x)

[Out]

16*x**4 - 24*x**3 + 89*x**2 - 60*x - exp(x)

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