3.35.55 \(\int \frac {1}{29} (-60-29 e^5+29 x) \, dx\)

Optimal. Leaf size=19 \[ \frac {1}{2} \left (-\frac {120}{29}+x\right ) x-e^5 (21+x) \]

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Rubi [A]  time = 0.00, antiderivative size = 16, normalized size of antiderivative = 0.84, number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {9} \begin {gather*} \frac {\left (-29 x+29 e^5+60\right )^2}{1682} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-60 - 29*E^5 + 29*x)/29,x]

[Out]

(60 + 29*E^5 - 29*x)^2/1682

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 (60+29 e^5-29 x\right )^2}{1682}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 19, normalized size = 1.00 \begin {gather*} -\frac {60 x}{29}-e^5 x+\frac {x^2}{2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-60 - 29*E^5 + 29*x)/29,x]

[Out]

(-60*x)/29 - E^5*x + x^2/2

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fricas [A]  time = 0.69, size = 14, normalized size = 0.74 \begin {gather*} \frac {1}{2} \, x^{2} - x e^{5} - \frac {60}{29} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(5)+x-60/29,x, algorithm="fricas")

[Out]

1/2*x^2 - x*e^5 - 60/29*x

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giac [A]  time = 0.11, size = 14, normalized size = 0.74 \begin {gather*} \frac {1}{2} \, x^{2} - x e^{5} - \frac {60}{29} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(5)+x-60/29,x, algorithm="giac")

[Out]

1/2*x^2 - x*e^5 - 60/29*x

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maple [A]  time = 0.02, size = 13, normalized size = 0.68

method	result	size
gosper	\(-\frac {x \left (-29 x +58 \,{\mathrm e}^{5}+120\right )}{58}\)	\(13\)
default	\(-x \,{\mathrm e}^{5}+\frac {x^{2}}{2}-\frac {60 x}{29}\)	\(15\)
norman	\(\left (-{\mathrm e}^{5}-\frac {60}{29}\right ) x +\frac {x^{2}}{2}\)	\(15\)
risch	\(-x \,{\mathrm e}^{5}+\frac {x^{2}}{2}-\frac {60 x}{29}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(5)+x-60/29,x,method=_RETURNVERBOSE)

[Out]

-1/58*x*(-29*x+58*exp(5)+120)

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maxima [A]  time = 0.47, size = 14, normalized size = 0.74 \begin {gather*} \frac {1}{2} \, x^{2} - x e^{5} - \frac {60}{29} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(5)+x-60/29,x, algorithm="maxima")

[Out]

1/2*x^2 - x*e^5 - 60/29*x

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mupad [B]  time = 0.02, size = 13, normalized size = 0.68 \begin {gather*} \frac {x^2}{2}-x\,\left ({\mathrm {e}}^5+\frac {60}{29}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x - exp(5) - 60/29,x)

[Out]

x^2/2 - x*(exp(5) + 60/29)

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sympy [A]  time = 0.05, size = 14, normalized size = 0.74 \begin {gather*} \frac {x^{2}}{2} + x \left (- e^{5} - \frac {60}{29}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(5)+x-60/29,x)

[Out]

x**2/2 + x*(-exp(5) - 60/29)

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