3.1240 \(\int (c+d x) \, dx\)

Optimal. Leaf size=12 \[ c x+\frac{d x^2}{2} \]

[Out]

c*x + (d*x^2)/2

_______________________________________________________________________________________

Rubi [A]  time = 0.00747544, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ c x+\frac{d x^2}{2} \]

Antiderivative was successfully verified.

[In]  Int[c + d*x,x]

[Out]

c*x + (d*x^2)/2

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ d \int x\, dx + \int c\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(d*x+c,x)

[Out]

d*Integral(x, x) + Integral(c, x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.000056637, size = 12, normalized size = 1. \[ c x+\frac{d x^2}{2} \]

Antiderivative was successfully verified.

[In]  Integrate[c + d*x,x]

[Out]

c*x + (d*x^2)/2

_______________________________________________________________________________________

Maple [A]  time = 0., size = 11, normalized size = 0.9 \[ cx+{\frac{d{x}^{2}}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(d*x+c,x)

[Out]

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

_______________________________________________________________________________________

Maxima [A]  time = 1.34011, size = 14, normalized size = 1.17 \[ \frac{1}{2} \, d x^{2} + c x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*d*x^2 + c*x

_______________________________________________________________________________________

Fricas [A]  time = 0.174211, size = 1, normalized size = 0.08 \[ \frac{1}{2} x^{2} d + x c \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*x^2*d + x*c

_______________________________________________________________________________________

Sympy [A]  time = 0.052889, size = 8, normalized size = 0.67 \[ c x + \frac{d x^{2}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(d*x+c,x)

[Out]

c*x + d*x**2/2

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.218852, size = 14, normalized size = 1.17 \[ \frac{1}{2} \, d x^{2} + c x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(d*x + c,x, algorithm="giac")

[Out]

1/2*d*x^2 + c*x