3.1031 \(\int (a+b x) \, dx\)

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

[Out]

a*x + (b*x^2)/2

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Rubi [A]  time = 0.00736761, 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. \[ a x+\frac{b x^2}{2} \]

Antiderivative was successfully verified.

[In]  Int[a + b*x,x]

[Out]

a*x + (b*x^2)/2

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(b*x+a,x)

[Out]

b*Integral(x, x) + Integral(a, x)

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Mathematica [A]  time = 0.0000419178, size = 12, normalized size = 1. \[ a x+\frac{b x^2}{2} \]

Antiderivative was successfully verified.

[In]  Integrate[a + b*x,x]

[Out]

a*x + (b*x^2)/2

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Maple [A]  time = 0.002, size = 11, normalized size = 0.9 \[ ax+{\frac{b{x}^{2}}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(b*x+a,x)

[Out]

a*x+1/2*b*x^2

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Maxima [A]  time = 1.3362, size = 14, normalized size = 1.17 \[ \frac{1}{2} \, b x^{2} + a x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(b*x + a,x, algorithm="maxima")

[Out]

1/2*b*x^2 + a*x

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Fricas [A]  time = 0.173978, size = 1, normalized size = 0.08 \[ \frac{1}{2} x^{2} b + x a \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(b*x + a,x, algorithm="fricas")

[Out]

1/2*x^2*b + x*a

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Sympy [A]  time = 0.05453, size = 8, normalized size = 0.67 \[ a x + \frac{b x^{2}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(b*x+a,x)

[Out]

a*x + b*x**2/2

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GIAC/XCAS [A]  time = 0.207881, size = 14, normalized size = 1.17 \[ \frac{1}{2} \, b x^{2} + a x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(b*x + a,x, algorithm="giac")

[Out]

1/2*b*x^2 + a*x