\(\int 3 a \, dx\) [8]

Optimal result

Integrand size = 3, antiderivative size = 4 \[ \int 3 a \, dx=3 a x \]

[Out]

3*a*x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {8} \[ \int 3 a \, dx=3 a x \]

[In]

Int[3*a,x]

[Out]

3*a*x

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps \begin{align*} \text {integral}& = 3 a x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int 3 a \, dx=3 a x \]

[In]

Integrate[3*a,x]

[Out]

3*a*x

Maple [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.25

method	result	size
default	\(3 a x\)	\(5\)
norman	\(3 a x\)	\(5\)
risch	\(3 a x\)	\(5\)
parallelrisch	\(3 a x\)	\(5\)

[In]

int(3*a,x,method=_RETURNVERBOSE)

[Out]

3*a*x

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int 3 a \, dx=3 \, a x \]

[In]

integrate(3*a,x, algorithm="fricas")

[Out]

3*a*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.75 \[ \int 3 a \, dx=3 a x \]

[In]

integrate(3*a,x)

[Out]

3*a*x

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int 3 a \, dx=3 \, a x \]

[In]

integrate(3*a,x, algorithm="maxima")

[Out]

3*a*x

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int 3 a \, dx=3 \, a x \]

[In]

integrate(3*a,x, algorithm="giac")

[Out]

3*a*x

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int 3 a \, dx=3\,a\,x \]

[In]

int(3*a,x)

[Out]

3*a*x