3.39.51 \(\int \frac {1}{2} (-1+e^2-e^{25}+2 x-9 x^2) \, dx\)

Optimal. Leaf size=21 \[ \frac {1}{2} x \left (-1+e^2-e^{25}+x-3 x^2\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.43, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {12} \begin {gather*} -\frac {3 x^3}{2}+\frac {x^2}{2}-\frac {1}{2} \left (1-e^2+e^{25}\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-1 + E^2 - E^25 + 2*x - 9*x^2)/2,x]

[Out]

-1/2*((1 - E^2 + E^25)*x) + x^2/2 - (3*x^3)/2

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (-1+e^2-e^{25}+2 x-9 x^2\right ) \, dx\\ &=-\frac {1}{2} \left (1-e^2+e^{25}\right ) x+\frac {x^2}{2}-\frac {3 x^3}{2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 27, normalized size = 1.29 \begin {gather*} \frac {1}{2} \left (-x+e^2 x-e^{25} x+x^2-3 x^3\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1 + E^2 - E^25 + 2*x - 9*x^2)/2,x]

[Out]

(-x + E^2*x - E^25*x + x^2 - 3*x^3)/2

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fricas [A]  time = 0.80, size = 24, normalized size = 1.14 \begin {gather*} -\frac {3}{2} \, x^{3} + \frac {1}{2} \, x^{2} - \frac {1}{2} \, x e^{25} + \frac {1}{2} \, x e^{2} - \frac {1}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/2*exp(25)+1/2*exp(2)-9/2*x^2+x-1/2,x, algorithm="fricas")

[Out]

-3/2*x^3 + 1/2*x^2 - 1/2*x*e^25 + 1/2*x*e^2 - 1/2*x

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giac [A]  time = 0.15, size = 24, normalized size = 1.14 \begin {gather*} -\frac {3}{2} \, x^{3} + \frac {1}{2} \, x^{2} - \frac {1}{2} \, x e^{25} + \frac {1}{2} \, x e^{2} - \frac {1}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/2*exp(25)+1/2*exp(2)-9/2*x^2+x-1/2,x, algorithm="giac")

[Out]

-3/2*x^3 + 1/2*x^2 - 1/2*x*e^25 + 1/2*x*e^2 - 1/2*x

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maple [A]  time = 0.02, size = 20, normalized size = 0.95

method	result	size
gosper	\(-\frac {x \left (3 x^{2}+{\mathrm e}^{25}-{\mathrm e}^{2}-x +1\right )}{2}\)	\(20\)
norman	\(\left (-\frac {{\mathrm e}^{25}}{2}+\frac {{\mathrm e}^{2}}{2}-\frac {1}{2}\right ) x +\frac {x^{2}}{2}-\frac {3 x^{3}}{2}\)	\(24\)
default	\(-\frac {x \,{\mathrm e}^{25}}{2}+\frac {{\mathrm e}^{2} x}{2}-\frac {3 x^{3}}{2}+\frac {x^{2}}{2}-\frac {x}{2}\)	\(25\)
risch	\(-\frac {x \,{\mathrm e}^{25}}{2}+\frac {{\mathrm e}^{2} x}{2}-\frac {3 x^{3}}{2}+\frac {x^{2}}{2}-\frac {x}{2}\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/2*exp(25)+1/2*exp(2)-9/2*x^2+x-1/2,x,method=_RETURNVERBOSE)

[Out]

-1/2*x*(3*x^2+exp(25)-exp(2)-x+1)

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maxima [A]  time = 0.35, size = 24, normalized size = 1.14 \begin {gather*} -\frac {3}{2} \, x^{3} + \frac {1}{2} \, x^{2} - \frac {1}{2} \, x e^{25} + \frac {1}{2} \, x e^{2} - \frac {1}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/2*exp(25)+1/2*exp(2)-9/2*x^2+x-1/2,x, algorithm="maxima")

[Out]

-3/2*x^3 + 1/2*x^2 - 1/2*x*e^25 + 1/2*x*e^2 - 1/2*x

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mupad [B]  time = 2.22, size = 19, normalized size = 0.90 \begin {gather*} -\frac {x\,\left (3\,x^2-x-{\mathrm {e}}^2+{\mathrm {e}}^{25}+1\right )}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x + exp(2)/2 - exp(25)/2 - (9*x^2)/2 - 1/2,x)

[Out]

-(x*(exp(25) - exp(2) - x + 3*x^2 + 1))/2

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sympy [A]  time = 0.05, size = 26, normalized size = 1.24 \begin {gather*} - \frac {3 x^{3}}{2} + \frac {x^{2}}{2} + x \left (- \frac {e^{25}}{2} - \frac {1}{2} + \frac {e^{2}}{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/2*exp(25)+1/2*exp(2)-9/2*x**2+x-1/2,x)

[Out]

-3*x**3/2 + x**2/2 + x*(-exp(25)/2 - 1/2 + exp(2)/2)

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