3.1549 \(\int \left (a+\frac{b}{x}\right ) x \, dx\)

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

[Out]

b*x + (a*x^2)/2

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Rubi [A]  time = 0.0134137, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{a x^2}{2}+b x \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x)*x,x]

[Out]

b*x + (a*x^2)/2

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x)*x,x)

[Out]

a*Integral(x, x) + Integral(b, x)

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Mathematica [A]  time = 0.000895952, size = 12, normalized size = 1. \[ \frac{a x^2}{2}+b x \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x)*x,x]

[Out]

b*x + (a*x^2)/2

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x)*x,x)

[Out]

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

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Maxima [A]  time = 1.433, size = 14, normalized size = 1.17 \[ \frac{1}{2} \, a x^{2} + b x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*a*x^2 + b*x

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Fricas [A]  time = 0.21299, size = 14, normalized size = 1.17 \[ \frac{1}{2} \, a x^{2} + b x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*a*x^2 + b*x

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Sympy [A]  time = 0.062622, size = 8, normalized size = 0.67 \[ \frac{a x^{2}}{2} + b x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x)*x,x)

[Out]

a*x**2/2 + b*x

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GIAC/XCAS [A]  time = 0.224759, size = 14, normalized size = 1.17 \[ \frac{1}{2} \, a x^{2} + b x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*a*x^2 + b*x