\(\int (c+d x) \, dx\) [1240]

Optimal result

Integrand size = 5, antiderivative size = 12 \[ \int (c+d x) \, dx=c x+\frac {d x^2}{2} \]

[Out]

c*x+1/2*d*x^2

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int (c+d x) \, dx=c x+\frac {d x^2}{2} \]

[In]

Int[c + d*x,x]

[Out]

c*x + (d*x^2)/2

Rubi steps \begin{align*} \text {integral}& = c x+\frac {d x^2}{2} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int (c+d x) \, dx=c x+\frac {d x^2}{2} \]

[In]

Integrate[c + d*x,x]

[Out]

c*x + (d*x^2)/2

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92

method	result	size
gosper	\(c x +\frac {1}{2} d \,x^{2}\)	\(11\)
default	\(c x +\frac {1}{2} d \,x^{2}\)	\(11\)
norman	\(c x +\frac {1}{2} d \,x^{2}\)	\(11\)
risch	\(c x +\frac {1}{2} d \,x^{2}\)	\(11\)
parallelrisch	\(c x +\frac {1}{2} d \,x^{2}\)	\(11\)
parts	\(c x +\frac {1}{2} d \,x^{2}\)	\(11\)

[In]

int(d*x+c,x,method=_RETURNVERBOSE)

[Out]

c*x+1/2*d*x^2

Fricas [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int (c+d x) \, dx=\frac {1}{2} x^{2} d + x c \]

[In]

integrate(d*x+c,x, algorithm="fricas")

[Out]

1/2*x^2*d + x*c

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int (c+d x) \, dx=c x + \frac {d x^{2}}{2} \]

[In]

integrate(d*x+c,x)

[Out]

c*x + d*x**2/2

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int (c+d x) \, dx=\frac {1}{2} \, d x^{2} + c x \]

[In]

integrate(d*x+c,x, algorithm="maxima")

[Out]

1/2*d*x^2 + c*x

Giac [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int (c+d x) \, dx=\frac {1}{2} \, d x^{2} + c x \]

[In]

integrate(d*x+c,x, algorithm="giac")

[Out]

1/2*d*x^2 + c*x

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int (c+d x) \, dx=\frac {d\,x^2}{2}+c\,x \]

[In]

int(c + d*x,x)

[Out]

c*x + (d*x^2)/2