3.79.36 \(\int \frac {1}{2} (-11-24 x) \, dx\)

Optimal. Leaf size=24 \[ \log \left (16 e^{-5-x-\frac {3}{2} \left (8+3 x+4 x^2\right )}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.46, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {9} \begin {gather*} -\frac {1}{96} (24 x+11)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-11 - 24*x)/2,x]

[Out]

-1/96*(11 + 24*x)^2

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}{96} (11+24 x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.46 \begin {gather*} -\frac {11 x}{2}-6 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-11 - 24*x)/2,x]

[Out]

(-11*x)/2 - 6*x^2

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fricas [A]  time = 0.51, size = 9, normalized size = 0.38 \begin {gather*} -6 \, x^{2} - \frac {11}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12*x-11/2,x, algorithm="fricas")

[Out]

-6*x^2 - 11/2*x

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giac [A]  time = 0.12, size = 9, normalized size = 0.38 \begin {gather*} -6 \, x^{2} - \frac {11}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12*x-11/2,x, algorithm="giac")

[Out]

-6*x^2 - 11/2*x

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maple [A]  time = 0.01, size = 9, normalized size = 0.38

method	result	size
gosper	\(-\frac {x \left (12 x +11\right )}{2}\)	\(9\)
default	\(-6 x^{2}-\frac {11}{2} x\)	\(10\)
norman	\(-6 x^{2}-\frac {11}{2} x\)	\(10\)
risch	\(-6 x^{2}-\frac {11}{2} x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-12*x-11/2,x,method=_RETURNVERBOSE)

[Out]

-1/2*x*(12*x+11)

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maxima [A]  time = 0.36, size = 9, normalized size = 0.38 \begin {gather*} -6 \, x^{2} - \frac {11}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12*x-11/2,x, algorithm="maxima")

[Out]

-6*x^2 - 11/2*x

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mupad [B]  time = 0.04, size = 8, normalized size = 0.33 \begin {gather*} -\frac {x\,\left (12\,x+11\right )}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 12*x - 11/2,x)

[Out]

-(x*(12*x + 11))/2

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sympy [A]  time = 0.05, size = 10, normalized size = 0.42 \begin {gather*} - 6 x^{2} - \frac {11 x}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12*x-11/2,x)

[Out]

-6*x**2 - 11*x/2

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