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

Optimal result

Integrand size = 11, antiderivative size = 10 \[ \int \left (-\frac {2}{x^2}+\frac {3}{x}\right ) \, dx=\frac {2}{x}+3 \log (x) \]

[Out]

2/x+3*ln(x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-\frac {2}{x^2}+\frac {3}{x}\right ) \, dx=\frac {2}{x}+3 \log (x) \]

[In]

Int[-2/x^2 + 3/x,x]

[Out]

2/x + 3*Log[x]

Rubi steps \begin{align*} \text {integral}& = \frac {2}{x}+3 \log (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \left (-\frac {2}{x^2}+\frac {3}{x}\right ) \, dx=\frac {2}{x}+3 \log (x) \]

[In]

Integrate[-2/x^2 + 3/x,x]

[Out]

2/x + 3*Log[x]

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 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	\(\frac {2}{x}+3 \ln \left (x \right )\)	\(11\)
parallelrisch	\(\frac {3 \ln \left (x \right ) x +2}{x}\)	\(12\)

[In]

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

[Out]

2/x+3*ln(x)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.10 \[ \int \left (-\frac {2}{x^2}+\frac {3}{x}\right ) \, dx=\frac {3 \, x \log \left (x\right ) + 2}{x} \]

[In]

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

[Out]

(3*x*log(x) + 2)/x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70 \[ \int \left (-\frac {2}{x^2}+\frac {3}{x}\right ) \, dx=3 \log {\left (x \right )} + \frac {2}{x} \]

[In]

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

[Out]

3*log(x) + 2/x

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \left (-\frac {2}{x^2}+\frac {3}{x}\right ) \, dx=\frac {2}{x} + 3 \, \log \left (x\right ) \]

[In]

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

[Out]

2/x + 3*log(x)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.10 \[ \int \left (-\frac {2}{x^2}+\frac {3}{x}\right ) \, dx=\frac {2}{x} + 3 \, \log \left ({\left | x \right |}\right ) \]

[In]

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

[Out]

2/x + 3*log(abs(x))

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \left (-\frac {2}{x^2}+\frac {3}{x}\right ) \, dx=3\,\ln \left (x\right )+\frac {2}{x} \]

[In]

int(3/x - 2/x^2,x)

[Out]

3*log(x) + 2/x