\(\int \frac {1}{5} (-738-360 x) \, dx\) [3424]

Optimal result

Integrand size = 9, antiderivative size = 21 \[ \int \frac {1}{5} (-738-360 x) \, dx=e^4+\frac {2 x}{5}-4 \left (1+x+(6+3 x)^2\right ) \]

[Out]

exp(4)-4*(6+3*x)^2-4-18/5*x

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} \[ \int \frac {1}{5} (-738-360 x) \, dx=-\frac {9}{100} (20 x+41)^2 \]

[In]

Int[(-738 - 360*x)/5,x]

[Out]

(-9*(41 + 20*x)^2)/100

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 {9}{100} (41+20 x)^2 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.52 \[ \int \frac {1}{5} (-738-360 x) \, dx=-\frac {738 x}{5}-36 x^2 \]

[In]

Integrate[(-738 - 360*x)/5,x]

[Out]

(-738*x)/5 - 36*x^2

Maple [A] (verified)

Time = 0.07 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.43

method	result	size
gosper	\(-\frac {18 x \left (10 x +41\right )}{5}\)	\(9\)
default	\(-36 x^{2}-\frac {738}{5} x\)	\(10\)
norman	\(-36 x^{2}-\frac {738}{5} x\)	\(10\)
risch	\(-36 x^{2}-\frac {738}{5} x\)	\(10\)
parallelrisch	\(-36 x^{2}-\frac {738}{5} x\)	\(10\)
parts	\(-36 x^{2}-\frac {738}{5} x\)	\(10\)

[In]

int(-72*x-738/5,x,method=_RETURNVERBOSE)

[Out]

-18/5*x*(10*x+41)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.43 \[ \int \frac {1}{5} (-738-360 x) \, dx=-36 \, x^{2} - \frac {738}{5} \, x \]

[In]

integrate(-72*x-738/5,x, algorithm="fricas")

[Out]

-36*x^2 - 738/5*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.48 \[ \int \frac {1}{5} (-738-360 x) \, dx=- 36 x^{2} - \frac {738 x}{5} \]

[In]

integrate(-72*x-738/5,x)

[Out]

-36*x**2 - 738*x/5

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.43 \[ \int \frac {1}{5} (-738-360 x) \, dx=-36 \, x^{2} - \frac {738}{5} \, x \]

[In]

integrate(-72*x-738/5,x, algorithm="maxima")

[Out]

-36*x^2 - 738/5*x

Giac [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.43 \[ \int \frac {1}{5} (-738-360 x) \, dx=-36 \, x^{2} - \frac {738}{5} \, x \]

[In]

integrate(-72*x-738/5,x, algorithm="giac")

[Out]

-36*x^2 - 738/5*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.38 \[ \int \frac {1}{5} (-738-360 x) \, dx=-\frac {18\,x\,\left (10\,x+41\right )}{5} \]

[In]

int(- 72*x - 738/5,x)

[Out]

-(18*x*(10*x + 41))/5