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

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

[Out]

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

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Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} c x+\frac {d x^2}{2} \end {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} c x+\frac {d x^2}{2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[c + d*x,x]

[Out]

c*x + (d*x^2)/2

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Maple [A]
time = 0.01, size = 11, normalized size = 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	\(c x +\frac {1}{2} d \,x^{2}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.31, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, d x^{2} + c x \end {gather*}

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 = 0.42, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{2} x^{2} d + x c \end {gather*}

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 = 0.01, size = 8, normalized size = 0.67 \begin {gather*} c x + \frac {d x^{2}}{2} \end {gather*}

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 = 1.13, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, d x^{2} + c x \end {gather*}

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

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Mupad [B]
time = 0.02, size = 10, normalized size = 0.83 \begin {gather*} \frac {d\,x^2}{2}+c\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(c + d*x,x)

[Out]

c*x + (d*x^2)/2

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