3.95.23 \(\int \frac {1}{5} (-81+5 e^2+22 x) \, dx\)

Optimal. Leaf size=20 \[ x \left (e^2+x-\frac {3}{5} (3 (9-x)+x)\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 16, normalized size of antiderivative = 0.80, 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 {1}{220} \left (-22 x-5 e^2+81\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-81 + 5*E^2 + 22*x)/5,x]

[Out]

(81 - 5*E^2 - 22*x)^2/220

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 {1}{220} \left (81-5 e^2-22 x\right )^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 18, normalized size = 0.90 \begin {gather*} -\frac {81 x}{5}+e^2 x+\frac {11 x^2}{5} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-81 + 5*E^2 + 22*x)/5,x]

[Out]

(-81*x)/5 + E^2*x + (11*x^2)/5

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fricas [A]  time = 0.58, size = 13, normalized size = 0.65 \begin {gather*} \frac {11}{5} \, x^{2} + x e^{2} - \frac {81}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(2)+22/5*x-81/5,x, algorithm="fricas")

[Out]

11/5*x^2 + x*e^2 - 81/5*x

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giac [A]  time = 0.23, size = 13, normalized size = 0.65 \begin {gather*} \frac {11}{5} \, x^{2} + x e^{2} - \frac {81}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(2)+22/5*x-81/5,x, algorithm="giac")

[Out]

11/5*x^2 + x*e^2 - 81/5*x

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maple [A]  time = 0.02, size = 13, normalized size = 0.65

method	result	size
gosper	\(\frac {x \left (11 x +5 \,{\mathrm e}^{2}-81\right )}{5}\)	\(13\)
norman	\(\left ({\mathrm e}^{2}-\frac {81}{5}\right ) x +\frac {11 x^{2}}{5}\)	\(13\)
default	\({\mathrm e}^{2} x +\frac {11 x^{2}}{5}-\frac {81 x}{5}\)	\(14\)
risch	\({\mathrm e}^{2} x +\frac {11 x^{2}}{5}-\frac {81 x}{5}\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(2)+22/5*x-81/5,x,method=_RETURNVERBOSE)

[Out]

1/5*x*(11*x+5*exp(2)-81)

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maxima [A]  time = 0.35, size = 13, normalized size = 0.65 \begin {gather*} \frac {11}{5} \, x^{2} + x e^{2} - \frac {81}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(2)+22/5*x-81/5,x, algorithm="maxima")

[Out]

11/5*x^2 + x*e^2 - 81/5*x

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mupad [B]  time = 0.05, size = 12, normalized size = 0.60 \begin {gather*} \frac {11\,x^2}{5}+\left ({\mathrm {e}}^2-\frac {81}{5}\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((22*x)/5 + exp(2) - 81/5,x)

[Out]

x*(exp(2) - 81/5) + (11*x^2)/5

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sympy [A]  time = 0.06, size = 14, normalized size = 0.70 \begin {gather*} \frac {11 x^{2}}{5} + x \left (- \frac {81}{5} + e^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(2)+22/5*x-81/5,x)

[Out]

11*x**2/5 + x*(-81/5 + exp(2))

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