\(\int (231-4 x) \, dx\) [7954]

Optimal result

Integrand size = 5, antiderivative size = 18 \[ \int (231-4 x) \, dx=6+231 x-2 x^2+2 (3-\log (3)) \]

[Out]

12-2*ln(3)+231*x-2*x^2

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.50, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int (231-4 x) \, dx=231 x-2 x^2 \]

[In]

Int[231 - 4*x,x]

[Out]

231*x - 2*x^2

Rubi steps \begin{align*} \text {integral}& = 231 x-2 x^2 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.50 \[ \int (231-4 x) \, dx=231 x-2 x^2 \]

[In]

Integrate[231 - 4*x,x]

[Out]

231*x - 2*x^2

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.50

method	result	size
gosper	\(-x \left (2 x -231\right )\)	\(9\)
default	\(-2 x^{2}+231 x\)	\(10\)
norman	\(-2 x^{2}+231 x\)	\(10\)
risch	\(-2 x^{2}+231 x\)	\(10\)
parallelrisch	\(-2 x^{2}+231 x\)	\(10\)
parts	\(-2 x^{2}+231 x\)	\(10\)

[In]

int(-4*x+231,x,method=_RETURNVERBOSE)

[Out]

-x*(2*x-231)

Fricas [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.50 \[ \int (231-4 x) \, dx=-2 \, x^{2} + 231 \, x \]

[In]

integrate(-4*x+231,x, algorithm="fricas")

[Out]

-2*x^2 + 231*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.39 \[ \int (231-4 x) \, dx=- 2 x^{2} + 231 x \]

[In]

integrate(-4*x+231,x)

[Out]

-2*x**2 + 231*x

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.50 \[ \int (231-4 x) \, dx=-2 \, x^{2} + 231 \, x \]

[In]

integrate(-4*x+231,x, algorithm="maxima")

[Out]

-2*x^2 + 231*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.50 \[ \int (231-4 x) \, dx=-2 \, x^{2} + 231 \, x \]

[In]

integrate(-4*x+231,x, algorithm="giac")

[Out]

-2*x^2 + 231*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.44 \[ \int (231-4 x) \, dx=-x\,\left (2\,x-231\right ) \]

[In]

int(231 - 4*x,x)

[Out]

-x*(2*x - 231)