\(\int (-\frac {3}{x^3}+\frac {4}{x^2}) \, dx\) [1908]

Optimal result

Integrand size = 11, antiderivative size = 13 \[ \int \left (-\frac {3}{x^3}+\frac {4}{x^2}\right ) \, dx=\frac {3}{2 x^2}-\frac {4}{x} \]

[Out]

3/2/x^2-4/x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 13, 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 = {} \[ \int \left (-\frac {3}{x^3}+\frac {4}{x^2}\right ) \, dx=\frac {3}{2 x^2}-\frac {4}{x} \]

[In]

Int[-3/x^3 + 4/x^2,x]

[Out]

3/(2*x^2) - 4/x

Rubi steps \begin{align*} \text {integral}& = \frac {3}{2 x^2}-\frac {4}{x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \left (-\frac {3}{x^3}+\frac {4}{x^2}\right ) \, dx=\frac {3}{2 x^2}-\frac {4}{x} \]

[In]

Integrate[-3/x^3 + 4/x^2,x]

[Out]

3/(2*x^2) - 4/x

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77

method	result	size
norman	\(\frac {-4 x +\frac {3}{2}}{x^{2}}\)	\(10\)
gosper	\(-\frac {8 x -3}{2 x^{2}}\)	\(11\)
parallelrisch	\(\frac {-8 x +3}{2 x^{2}}\)	\(11\)
default	\(\frac {3}{2 x^{2}}-\frac {4}{x}\)	\(12\)
risch	\(\frac {3}{2 x^{2}}-\frac {4}{x}\)	\(12\)

[In]

int(-3/x^3+4/x^2,x,method=_RETURNVERBOSE)

[Out]

(-4*x+3/2)/x^2

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \left (-\frac {3}{x^3}+\frac {4}{x^2}\right ) \, dx=-\frac {8 \, x - 3}{2 \, x^{2}} \]

[In]

integrate(-3/x^3+4/x^2,x, algorithm="fricas")

[Out]

-1/2*(8*x - 3)/x^2

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.62 \[ \int \left (-\frac {3}{x^3}+\frac {4}{x^2}\right ) \, dx=\frac {3 - 8 x}{2 x^{2}} \]

[In]

integrate(-3/x**3+4/x**2,x)

[Out]

(3 - 8*x)/(2*x**2)

Maxima [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.85 \[ \int \left (-\frac {3}{x^3}+\frac {4}{x^2}\right ) \, dx=-\frac {4}{x} + \frac {3}{2 \, x^{2}} \]

[In]

integrate(-3/x^3+4/x^2,x, algorithm="maxima")

[Out]

-4/x + 3/2/x^2

Giac [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.85 \[ \int \left (-\frac {3}{x^3}+\frac {4}{x^2}\right ) \, dx=-\frac {4}{x} + \frac {3}{2 \, x^{2}} \]

[In]

integrate(-3/x^3+4/x^2,x, algorithm="giac")

[Out]

-4/x + 3/2/x^2

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \left (-\frac {3}{x^3}+\frac {4}{x^2}\right ) \, dx=-\frac {8\,x-3}{2\,x^2} \]

[In]

int(4/x^2 - 3/x^3,x)

[Out]

-(8*x - 3)/(2*x^2)