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

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Rubi [A]  time = 0.0021542, 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., Rules used = {} \[ c x+\frac{d x^2}{2} \]

Antiderivative was successfully verified.

[In]

Int[c + d*x,x]

[Out]

c*x + (d*x^2)/2

Rubi steps

\begin{align*} \int (c+d x) \, dx &=c x+\frac{d x^2}{2}\\ \end{align*}

Mathematica [A]  time = 0.000037, 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

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Maple [A]  time = 0.001, size = 11, normalized size = 0.9 \begin{align*} cx+{\frac{d{x}^{2}}{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(d*x+c,x)

[Out]

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

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Maxima [A]  time = 0.94133, size = 14, normalized size = 1.17 \begin{align*} \frac{1}{2} \, d x^{2} + c x \end{align*}

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

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Fricas [A]  time = 1.74649, size = 23, normalized size = 1.92 \begin{align*} \frac{1}{2} x^{2} d + x c \end{align*}

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

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Sympy [A]  time = 0.050014, size = 8, normalized size = 0.67 \begin{align*} c x + \frac{d x^{2}}{2} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(d*x+c,x)

[Out]

c*x + d*x**2/2

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Giac [A]  time = 1.05364, size = 14, normalized size = 1.17 \begin{align*} \frac{1}{2} \, d x^{2} + c x \end{align*}

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