3.47 \(\int \frac{a+b x}{x} \, dx\)

Optimal. Leaf size=8 \[ a \log (x)+b x \]

[Out]

b*x + a*Log[x]

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Rubi [A]  time = 0.00984268, antiderivative size = 8, 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 \[ a \log (x)+b x \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)/x,x]

[Out]

b*x + a*Log[x]

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ a \log{\left (x \right )} + \int b\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x+a)/x,x)

[Out]

a*log(x) + Integral(b, x)

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Mathematica [A]  time = 0.0012073, size = 8, normalized size = 1. \[ a \log (x)+b x \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)/x,x]

[Out]

b*x + a*Log[x]

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Maple [A]  time = 0.018, size = 9, normalized size = 1.1 \[ bx+a\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)/x,x)

[Out]

b*x+a*ln(x)

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Maxima [A]  time = 1.31491, size = 11, normalized size = 1.38 \[ b x + a \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b*x + a*log(x)

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Fricas [A]  time = 0.201153, size = 11, normalized size = 1.38 \[ b x + a \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b*x + a*log(x)

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Sympy [A]  time = 0.130943, size = 7, normalized size = 0.88 \[ a \log{\left (x \right )} + b x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)/x,x)

[Out]

a*log(x) + b*x

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GIAC/XCAS [A]  time = 0.212955, size = 12, normalized size = 1.5 \[ b x + a{\rm ln}\left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b*x + a*ln(abs(x))