3.20.5 \(\int (-\frac {2}{x^2}+\frac {3}{x}) \, dx\) [1905]

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

[Out]

2/x+3*ln(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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Mathics [A]
time = 1.63, size = 10, normalized size = 1.00 \begin {gather*} \frac {2}{x}+3 \text {Log}\left [x\right ] \end {gather*}

Antiderivative was successfully verified.

[In]

mathics('Integrate[-2/x^2 + 3/x,x]')

[Out]

2 / x + 3 Log[x]

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Maple [A]
time = 0.01, size = 11, normalized size = 1.10

method	result	size
default	\(\frac {2}{x}+3 \ln \left (x \right )\)	\(11\)
norman	\(\frac {2}{x}+3 \ln \left (x \right )\)	\(11\)
risch	\(\frac {2}{x}+3 \ln \left (x \right )\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2/x^2+3/x,x,method=_RETURNVERBOSE)

[Out]

2/x+3*ln(x)

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Maxima [A]
time = 0.26, size = 10, normalized size = 1.00 \begin {gather*} \frac {2}{x} + 3 \, \log \left (x\right ) \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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Fricas [A]
time = 0.29, size = 11, normalized size = 1.10 \begin {gather*} \frac {3 \, x \log \left (x\right ) + 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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Sympy [A]
time = 0.04, size = 7, normalized size = 0.70 \begin {gather*} 3 \log {\left (x \right )} + \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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Giac [A]
time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} \frac {2}{x}+3 \ln \left |x\right | \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2/x + 3*log(abs(x))

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Mupad [B]
time = 0.03, size = 10, normalized size = 1.00 \begin {gather*} 3\,\ln \left (x\right )+\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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