3.19.1 \(\int \frac {1}{2} (17-3 e+12 x) \, dx\)

Optimal. Leaf size=15 \[ x+\frac {3}{2} x (5-e+2 x) \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.93, number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {9} \begin {gather*} \frac {1}{48} (12 x-3 e+17)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(17 - 3*E + 12*x)/2,x]

[Out]

(17 - 3*E + 12*x)^2/48

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}{48} (17-3 e+12 x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 17, normalized size = 1.13 \begin {gather*} \frac {17 x}{2}-\frac {3 e x}{2}+3 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(17 - 3*E + 12*x)/2,x]

[Out]

(17*x)/2 - (3*E*x)/2 + 3*x^2

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fricas [A]  time = 1.15, size = 14, normalized size = 0.93 \begin {gather*} 3 \, x^{2} - \frac {3}{2} \, x e + \frac {17}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/2*exp(1)+6*x+17/2,x, algorithm="fricas")

[Out]

3*x^2 - 3/2*x*e + 17/2*x

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giac [A]  time = 0.32, size = 14, normalized size = 0.93 \begin {gather*} 3 \, x^{2} - \frac {3}{2} \, x e + \frac {17}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/2*exp(1)+6*x+17/2,x, algorithm="giac")

[Out]

3*x^2 - 3/2*x*e + 17/2*x

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maple [A]  time = 0.02, size = 13, normalized size = 0.87

method	result	size
gosper	\(-\frac {x \left (-6 x +3 \,{\mathrm e}-17\right )}{2}\)	\(13\)
default	\(-\frac {3 x \,{\mathrm e}}{2}+3 x^{2}+\frac {17 x}{2}\)	\(15\)
norman	\(\left (-\frac {3 \,{\mathrm e}}{2}+\frac {17}{2}\right ) x +3 x^{2}\)	\(15\)
risch	\(-\frac {3 x \,{\mathrm e}}{2}+3 x^{2}+\frac {17 x}{2}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3/2*exp(1)+6*x+17/2,x,method=_RETURNVERBOSE)

[Out]

-1/2*x*(-6*x+3*exp(1)-17)

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maxima [A]  time = 0.74, size = 14, normalized size = 0.93 \begin {gather*} 3 \, x^{2} - \frac {3}{2} \, x e + \frac {17}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/2*exp(1)+6*x+17/2,x, algorithm="maxima")

[Out]

3*x^2 - 3/2*x*e + 17/2*x

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mupad [B]  time = 0.04, size = 12, normalized size = 0.80 \begin {gather*} \frac {x\,\left (6\,x-3\,\mathrm {e}+17\right )}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*x - (3*exp(1))/2 + 17/2,x)

[Out]

(x*(6*x - 3*exp(1) + 17))/2

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sympy [A]  time = 0.05, size = 15, normalized size = 1.00 \begin {gather*} 3 x^{2} + x \left (\frac {17}{2} - \frac {3 e}{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/2*exp(1)+6*x+17/2,x)

[Out]

3*x**2 + x*(17/2 - 3*E/2)

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