3.73.41 $\int (50+e^{3-x}(-1+x)+292x+381x^2+140x^3+15x^4)dx$

Optimal. Leaf size=30 $$x(-e^{3-x}+x+(3+\frac{2}{x})x(1+x)(5+x{)}^2)$$

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Rubi [A]  time = 0.02, antiderivative size = 46, normalized size of antiderivative = 1.53, number of steps used = 3, number of rules used = 2, integrand size = 31, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.065, Rules used = {2176, 2194} $$\begin{array}{c}3x^5+35x^4+127x^3+146x^2+50x-e^{3-x}+e^{3-x}(1-x)\end{array}$$

Antiderivative was successfully verified.

[In]

Int[50 + E^(3 - x)*(-1 + x) + 292*x + 381*x^2 + 140*x^3 + 15*x^4,x]

[Out]

-E^(3 - x) + E^(3 - x)*(1 - x) + 50*x + 146*x^2 + 127*x^3 + 35*x^4 + 3*x^5

Rule 2176

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[((c + d*x)^m
*(b*F^(g*(e + f*x)))^n)/(f*g*n*Log[F]), x] - Dist[(d*m)/(f*g*n*Log[F]), Int[(c + d*x)^(m - 1)*(b*F^(g*(e + f*x
)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && GtQ[m, 0] && IntegerQ[2*m] &&  !$UseGamma === True

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =50x+146x^2+127x^3+35x^4+3x^5+\int e^{3-x}(-1+x)dx\\ & =e^{3-x}(1-x)+50x+146x^2+127x^3+35x^4+3x^5+\int e^{3-x}dx\\ & =-e^{3-x}+e^{3-x}(1-x)+50x+146x^2+127x^3+35x^4+3x^5\end{array}\end{array}$$

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Mathematica [A]  time = 0.02, size = 34, normalized size = 1.13 $$\begin{array}{c}50x-e^{3-x}x+146x^2+127x^3+35x^4+3x^5\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[50 + E^(3 - x)*(-1 + x) + 292*x + 381*x^2 + 140*x^3 + 15*x^4,x]

[Out]

50*x - E^(3 - x)*x + 146*x^2 + 127*x^3 + 35*x^4 + 3*x^5

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fricas [A]  time = 0.73, size = 33, normalized size = 1.10 $$\begin{array}{c}3x^5+35x^4+127x^3+146x^2-x{e}^{(-x+3)}+50x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x-1)*exp(3-x)+15*x^4+140*x^3+381*x^2+292*x+50,x, algorithm="fricas")

[Out]

3*x^5 + 35*x^4 + 127*x^3 + 146*x^2 - x*e^(-x + 3) + 50*x

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giac [A]  time = 0.15, size = 33, normalized size = 1.10 $$\begin{array}{c}3x^5+35x^4+127x^3+146x^2-x{e}^{(-x+3)}+50x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x-1)*exp(3-x)+15*x^4+140*x^3+381*x^2+292*x+50,x, algorithm="giac")

[Out]

3*x^5 + 35*x^4 + 127*x^3 + 146*x^2 - x*e^(-x + 3) + 50*x

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maple [A]  time = 0.02, size = 34, normalized size = 1.13

method	result	size
norman	$50x+146x^2+127x^3+35x^4+3x^5-x{\mathrm{e}}^{3-x}$	$34$
risch	$50x+146x^2+127x^3+35x^4+3x^5-x{\mathrm{e}}^{3-x}$	$34$
default	$50x+{\mathrm{e}}^{3-x}(3-x)-3{\mathrm{e}}^{3-x}+146x^2+127x^3+35x^4+3x^5$	$45$
derivativedivides	$146{(3-x)}^2-2778+926x+127x^3+35x^4+3x^5+{\mathrm{e}}^{3-x}(3-x)-3{\mathrm{e}}^{3-x}$	$50$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x-1)*exp(3-x)+15*x^4+140*x^3+381*x^2+292*x+50,x,method=_RETURNVERBOSE)

[Out]

50*x+146*x^2+127*x^3+35*x^4+3*x^5-x*exp(3-x)

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maxima [A]  time = 0.36, size = 33, normalized size = 1.10 $$\begin{array}{c}3x^5+35x^4+127x^3+146x^2-x{e}^{(-x+3)}+50x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x-1)*exp(3-x)+15*x^4+140*x^3+381*x^2+292*x+50,x, algorithm="maxima")

[Out]

3*x^5 + 35*x^4 + 127*x^3 + 146*x^2 - x*e^(-x + 3) + 50*x

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mupad [B]  time = 0.06, size = 30, normalized size = 1.00 $$\begin{array}{c}x(146x-{\mathrm{e}}^{3-x}+127x^2+35x^3+3x^4+50)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(292*x + exp(3 - x)*(x - 1) + 381*x^2 + 140*x^3 + 15*x^4 + 50,x)

[Out]

x*(146*x - exp(3 - x) + 127*x^2 + 35*x^3 + 3*x^4 + 50)

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sympy [A]  time = 0.11, size = 29, normalized size = 0.97 $$\begin{array}{c}3x^5+35x^4+127x^3+146x^2-x{e}^{3-x}+50x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x-1)*exp(3-x)+15*x**4+140*x**3+381*x**2+292*x+50,x)

[Out]

3*x**5 + 35*x**4 + 127*x**3 + 146*x**2 - x*exp(3 - x) + 50*x

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