3.1905 \(\int (-\frac{2}{x^2}+\frac{3}{x}) \, dx\)

Optimal. Leaf size=10 \[ \frac{2}{x}+3 \log (x) \]

[Out]

2/x + 3*Log[x]

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Rubi [A]  time = 0.0017358, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{2}{x}+3 \log (x) \]

Antiderivative was successfully verified.

[In]

Int[-2/x^2 + 3/x,x]

[Out]

2/x + 3*Log[x]

Rubi steps

\begin{align*} \int \left (-\frac{2}{x^2}+\frac{3}{x}\right ) \, dx &=\frac{2}{x}+3 \log (x)\\ \end{align*}

Mathematica [A]  time = 0.0013866, size = 10, normalized size = 1. \[ \frac{2}{x}+3 \log (x) \]

Antiderivative was successfully verified.

[In]

Integrate[-2/x^2 + 3/x,x]

[Out]

2/x + 3*Log[x]

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Maple [A]  time = 0.001, size = 11, normalized size = 1.1 \begin{align*} 2\,{x}^{-1}+3\,\ln \left ( x \right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2/x^2+3/x,x)

[Out]

2/x+3*ln(x)

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Maxima [A]  time = 0.948475, size = 14, normalized size = 1.4 \begin{align*} \frac{2}{x} + 3 \, \log \left (x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/x^2+3/x,x, algorithm="maxima")

[Out]

2/x + 3*log(x)

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Fricas [A]  time = 1.95024, size = 27, normalized size = 2.7 \begin{align*} \frac{3 \, x \log \left (x\right ) + 2}{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/x^2+3/x,x, algorithm="fricas")

[Out]

(3*x*log(x) + 2)/x

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Sympy [A]  time = 0.075587, size = 7, normalized size = 0.7 \begin{align*} 3 \log{\left (x \right )} + \frac{2}{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/x**2+3/x,x)

[Out]

3*log(x) + 2/x

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Giac [A]  time = 1.05383, size = 15, normalized size = 1.5 \begin{align*} \frac{2}{x} + 3 \, \log \left ({\left | x \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/x^2+3/x,x, algorithm="giac")

[Out]

2/x + 3*log(abs(x))