3.37.13 \(\int \frac {1}{125} (-2 e^5+250 x) \, dx\) [3613]

Optimal. Leaf size=19 \[ -3 e^3+\left (\frac {e^5}{125}-x\right )^2 \]

[Out]

(1/125*exp(5)-x)^2-3*exp(3)

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Rubi [A]
time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.68, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {9} \begin {gather*} \frac {\left (e^5-125 x\right )^2}{15625} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-2*E^5 + 250*x)/125,x]

[Out]

(E^5 - 125*x)^2/15625

Rule 9

Int[(a_)*((b_) + (c_.)*(x_)), x_Symbol] :> Simp[a*((b + c*x)^2/(2*c)), x] /; FreeQ[{a, b, c}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\left (e^5-125 x\right )^2}{15625}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 12, normalized size = 0.63 \begin {gather*} -\frac {2 e^5 x}{125}+x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2*E^5 + 250*x)/125,x]

[Out]

(-2*E^5*x)/125 + x^2

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Maple [A]
time = 0.14, size = 10, normalized size = 0.53

method	result	size
default	\(-\frac {2 x \,{\mathrm e}^{5}}{125}+x^{2}\)	\(10\)
norman	\(-\frac {2 x \,{\mathrm e}^{5}}{125}+x^{2}\)	\(10\)
risch	\(-\frac {2 x \,{\mathrm e}^{5}}{125}+x^{2}\)	\(10\)
gosper	\(-\frac {x \left (-125 x +2 \,{\mathrm e}^{5}\right )}{125}\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2/125*exp(5)+2*x,x,method=_RETURNVERBOSE)

[Out]

-2/125*x*exp(5)+x^2

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Maxima [A]
time = 0.26, size = 9, normalized size = 0.47 \begin {gather*} x^{2} - \frac {2}{125} \, x e^{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/125*exp(5)+2*x,x, algorithm="maxima")

[Out]

x^2 - 2/125*x*e^5

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Fricas [A]
time = 0.33, size = 9, normalized size = 0.47 \begin {gather*} x^{2} - \frac {2}{125} \, x e^{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/125*exp(5)+2*x,x, algorithm="fricas")

[Out]

x^2 - 2/125*x*e^5

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Sympy [A]
time = 0.01, size = 10, normalized size = 0.53 \begin {gather*} x^{2} - \frac {2 x e^{5}}{125} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/125*exp(5)+2*x,x)

[Out]

x**2 - 2*x*exp(5)/125

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Giac [A]
time = 0.40, size = 9, normalized size = 0.47 \begin {gather*} x^{2} - \frac {2}{125} \, x e^{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/125*exp(5)+2*x,x, algorithm="giac")

[Out]

x^2 - 2/125*x*e^5

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Mupad [B]
time = 0.03, size = 9, normalized size = 0.47 \begin {gather*} x^2-\frac {2\,x\,{\mathrm {e}}^5}{125} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x - (2*exp(5))/125,x)

[Out]

x^2 - (2*x*exp(5))/125

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