\(\int \frac {1}{25} (92-2 x) \, dx\) [5110]

Optimal result

Integrand size = 9, antiderivative size = 21 \[ \int \frac {1}{25} (92-2 x) \, dx=6-e+2 x-\left (-5+\frac {4+x}{5}\right )^2 \]

[Out]

6-(-21/5+1/5*x)^2+2*x-exp(1)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.52, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {9} \[ \int \frac {1}{25} (92-2 x) \, dx=-\frac {1}{25} (46-x)^2 \]

[In]

Int[(92 - 2*x)/25,x]

[Out]

-1/25*(46 - 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}{25} (46-x)^2 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.71 \[ \int \frac {1}{25} (92-2 x) \, dx=-\frac {2}{25} \left (-46 x+\frac {x^2}{2}\right ) \]

[In]

Integrate[(92 - 2*x)/25,x]

[Out]

(-2*(-46*x + x^2/2))/25

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.33

method	result	size
gosper	\(-\frac {x \left (x -92\right )}{25}\)	\(7\)
default	\(-\frac {1}{25} x^{2}+\frac {92}{25} x\)	\(10\)
norman	\(-\frac {1}{25} x^{2}+\frac {92}{25} x\)	\(10\)
risch	\(-\frac {1}{25} x^{2}+\frac {92}{25} x\)	\(10\)
parallelrisch	\(-\frac {1}{25} x^{2}+\frac {92}{25} x\)	\(10\)
parts	\(-\frac {1}{25} x^{2}+\frac {92}{25} x\)	\(10\)

[In]

int(-2/25*x+92/25,x,method=_RETURNVERBOSE)

[Out]

-1/25*x*(x-92)

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.43 \[ \int \frac {1}{25} (92-2 x) \, dx=-\frac {1}{25} \, x^{2} + \frac {92}{25} \, x \]

[In]

integrate(-2/25*x+92/25,x, algorithm="fricas")

[Out]

-1/25*x^2 + 92/25*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.38 \[ \int \frac {1}{25} (92-2 x) \, dx=- \frac {x^{2}}{25} + \frac {92 x}{25} \]

[In]

integrate(-2/25*x+92/25,x)

[Out]

-x**2/25 + 92*x/25

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.43 \[ \int \frac {1}{25} (92-2 x) \, dx=-\frac {1}{25} \, x^{2} + \frac {92}{25} \, x \]

[In]

integrate(-2/25*x+92/25,x, algorithm="maxima")

[Out]

-1/25*x^2 + 92/25*x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.43 \[ \int \frac {1}{25} (92-2 x) \, dx=-\frac {1}{25} \, x^{2} + \frac {92}{25} \, x \]

[In]

integrate(-2/25*x+92/25,x, algorithm="giac")

[Out]

-1/25*x^2 + 92/25*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.29 \[ \int \frac {1}{25} (92-2 x) \, dx=-\frac {x\,\left (x-92\right )}{25} \]

[In]

int(92/25 - (2*x)/25,x)

[Out]

-(x*(x - 92))/25