\(\int -\frac {18 x}{25} \, dx\) [6222]

Optimal result

Integrand size = 5, antiderivative size = 16 \[ \int -\frac {18 x}{25} \, dx=5+25 e^{-32+e}-\frac {9 x^2}{25} \]

[Out]

25/exp(32-exp(1))+5-9/25*x^2

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {12, 30} \[ \int -\frac {18 x}{25} \, dx=-\frac {9 x^2}{25} \]

[In]

Int[(-18*x)/25,x]

[Out]

(-9*x^2)/25

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps \begin{align*} \text {integral}& = -\frac {18 \int x \, dx}{25} \\ & = -\frac {9 x^2}{25} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44 \[ \int -\frac {18 x}{25} \, dx=-\frac {9 x^2}{25} \]

[In]

Integrate[(-18*x)/25,x]

[Out]

(-9*x^2)/25

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.38

method	result	size
gosper	\(-\frac {9 x^{2}}{25}\)	\(6\)
default	\(-\frac {9 x^{2}}{25}\)	\(6\)
norman	\(-\frac {9 x^{2}}{25}\)	\(6\)
risch	\(-\frac {9 x^{2}}{25}\)	\(6\)
parallelrisch	\(-\frac {9 x^{2}}{25}\)	\(6\)

[In]

int(-18/25*x,x,method=_RETURNVERBOSE)

[Out]

-9/25*x^2

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -\frac {18 x}{25} \, dx=-\frac {9}{25} \, x^{2} \]

[In]

integrate(-18/25*x,x, algorithm="fricas")

[Out]

-9/25*x^2

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44 \[ \int -\frac {18 x}{25} \, dx=- \frac {9 x^{2}}{25} \]

[In]

integrate(-18/25*x,x)

[Out]

-9*x**2/25

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -\frac {18 x}{25} \, dx=-\frac {9}{25} \, x^{2} \]

[In]

integrate(-18/25*x,x, algorithm="maxima")

[Out]

-9/25*x^2

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -\frac {18 x}{25} \, dx=-\frac {9}{25} \, x^{2} \]

[In]

integrate(-18/25*x,x, algorithm="giac")

[Out]

-9/25*x^2

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -\frac {18 x}{25} \, dx=-\frac {9\,x^2}{25} \]

[In]

int(-(18*x)/25,x)

[Out]

-(9*x^2)/25