\(\int \frac {1}{2} (-11-24 x) \, dx\) [7836]

Optimal result

Integrand size = 9, antiderivative size = 24 \[ \int \frac {1}{2} (-11-24 x) \, dx=\log \left (16 e^{-5-x-\frac {3}{2} \left (8+3 x+4 x^2\right )}\right ) \]

[Out]

ln(16/exp(6*x^2+11/2*x+17))

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.46, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {9} \[ \int \frac {1}{2} (-11-24 x) \, dx=-\frac {1}{96} (24 x+11)^2 \]

[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{align*} \text {integral}& = -\frac {1}{96} (11+24 x)^2 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.46 \[ \int \frac {1}{2} (-11-24 x) \, dx=-\frac {11 x}{2}-6 x^2 \]

[In]

Integrate[(-11 - 24*x)/2,x]

[Out]

(-11*x)/2 - 6*x^2

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 9, normalized size of antiderivative = 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	\(-6 x^{2}-\frac {11}{2} x\)	\(10\)
parallelrisch	\(-6 x^{2}-\frac {11}{2} x\)	\(10\)
parts	\(-6 x^{2}-\frac {11}{2} x\)	\(10\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.38 \[ \int \frac {1}{2} (-11-24 x) \, dx=-6 \, x^{2} - \frac {11}{2} \, x \]

[In]

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

[Out]

-6*x^2 - 11/2*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.42 \[ \int \frac {1}{2} (-11-24 x) \, dx=- 6 x^{2} - \frac {11 x}{2} \]

[In]

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

[Out]

-6*x**2 - 11*x/2

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.38 \[ \int \frac {1}{2} (-11-24 x) \, dx=-6 \, x^{2} - \frac {11}{2} \, x \]

[In]

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

[Out]

-6*x^2 - 11/2*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.38 \[ \int \frac {1}{2} (-11-24 x) \, dx=-6 \, x^{2} - \frac {11}{2} \, x \]

[In]

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

[Out]

-6*x^2 - 11/2*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.33 \[ \int \frac {1}{2} (-11-24 x) \, dx=-\frac {x\,\left (12\,x+11\right )}{2} \]

[In]

int(- 12*x - 11/2,x)

[Out]

-(x*(12*x + 11))/2