\(\int \frac {1}{3} (-5+6 x) \, dx\) [2334]

Optimal result

Integrand size = 9, antiderivative size = 15 \[ \int \frac {1}{3} (-5+6 x) \, dx=-1-\frac {1}{e}-\frac {5 x}{3}+x^2 \]

[Out]

-5/3*x-1+x^2-exp(-1)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {9} \[ \int \frac {1}{3} (-5+6 x) \, dx=\frac {1}{36} (5-6 x)^2 \]

[In]

Int[(-5 + 6*x)/3,x]

[Out]

(5 - 6*x)^2/36

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}{36} (5-6 x)^2 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.60 \[ \int \frac {1}{3} (-5+6 x) \, dx=-\frac {5 x}{3}+x^2 \]

[In]

Integrate[(-5 + 6*x)/3,x]

[Out]

(-5*x)/3 + x^2

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53

method	result	size
default	\(x^{2}-\frac {5}{3} x\)	\(8\)
norman	\(x^{2}-\frac {5}{3} x\)	\(8\)
risch	\(x^{2}-\frac {5}{3} x\)	\(8\)
parallelrisch	\(x^{2}-\frac {5}{3} x\)	\(8\)
parts	\(x^{2}-\frac {5}{3} x\)	\(8\)
gosper	\(\frac {x \left (3 x -5\right )}{3}\)	\(9\)

[In]

int(2*x-5/3,x,method=_RETURNVERBOSE)

[Out]

x^2-5/3*x

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.47 \[ \int \frac {1}{3} (-5+6 x) \, dx=x^{2} - \frac {5}{3} \, x \]

[In]

integrate(2*x-5/3,x, algorithm="fricas")

[Out]

x^2 - 5/3*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.47 \[ \int \frac {1}{3} (-5+6 x) \, dx=x^{2} - \frac {5 x}{3} \]

[In]

integrate(2*x-5/3,x)

[Out]

x**2 - 5*x/3

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.47 \[ \int \frac {1}{3} (-5+6 x) \, dx=x^{2} - \frac {5}{3} \, x \]

[In]

integrate(2*x-5/3,x, algorithm="maxima")

[Out]

x^2 - 5/3*x

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.47 \[ \int \frac {1}{3} (-5+6 x) \, dx=x^{2} - \frac {5}{3} \, x \]

[In]

integrate(2*x-5/3,x, algorithm="giac")

[Out]

x^2 - 5/3*x

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int \frac {1}{3} (-5+6 x) \, dx=\frac {x\,\left (3\,x-5\right )}{3} \]

[In]

int(2*x - 5/3,x)

[Out]

(x*(3*x - 5))/3