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

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

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {2}{x}+3 \log (x) \end {gather*}

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*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} \frac {2}{x}+3 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-2/x^2 + 3/x,x]

[Out]

2/x + 3*Log[x]

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (-\frac {2}{x^2}+\frac {3}{x}\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[-2/x^2 + 3/x,x]

[Out]

IntegrateAlgebraic[-2/x^2 + 3/x, x]

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fricas [A]  time = 1.02, size = 11, normalized size = 1.10 \begin {gather*} \frac {3 \, x \log \relax (x) + 2}{x} \end {gather*}

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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giac [A]  time = 1.12, size = 11, normalized size = 1.10 \begin {gather*} \frac {2}{x} + 3 \, \log \left ({\left | x \right |}\right ) \end {gather*}

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))

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maple [A]  time = 0.00, size = 11, normalized size = 1.10 \begin {gather*} 3 \ln \relax (x )+\frac {2}{x} \end {gather*}

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 = 1.03, size = 10, normalized size = 1.00 \begin {gather*} \frac {2}{x} + 3 \, \log \relax (x) \end {gather*}

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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mupad [B]  time = 0.03, size = 10, normalized size = 1.00 \begin {gather*} 3\,\ln \relax (x)+\frac {2}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3/x - 2/x^2,x)

[Out]

3*log(x) + 2/x

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sympy [A]  time = 0.08, size = 7, normalized size = 0.70 \begin {gather*} 3 \log {\relax (x )} + \frac {2}{x} \end {gather*}

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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