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

Optimal. Leaf size=13 \[ \frac {3}{2 x^2}-\frac {4}{x} \]

[Out]

3/2/x^2-4/x

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Rubi [A]
time = 0.00, antiderivative size = 13, 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 {3}{2 x^2}-\frac {4}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-3/x^3 + 4/x^2,x]

[Out]

3/(2*x^2) - 4/x

Rubi steps

\begin {align*} \int \left (-\frac {3}{x^3}+\frac {4}{x^2}\right ) \, dx &=\frac {3}{2 x^2}-\frac {4}{x}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {3}{2 x^2}-\frac {4}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-3/x^3 + 4/x^2,x]

[Out]

3/(2*x^2) - 4/x

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Maple [A]
time = 0.01, size = 12, normalized size = 0.92

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/2/x^2-4/x

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Maxima [A]
time = 0.29, size = 11, normalized size = 0.85 \begin {gather*} -\frac {4}{x} + \frac {3}{2 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-4/x + 3/2/x^2

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Fricas [A]
time = 0.58, size = 10, normalized size = 0.77 \begin {gather*} -\frac {8 \, x - 3}{2 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/2*(8*x - 3)/x^2

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Sympy [A]
time = 0.02, size = 8, normalized size = 0.62 \begin {gather*} \frac {3 - 8 x}{2 x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(3 - 8*x)/(2*x**2)

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Giac [A]
time = 1.57, size = 11, normalized size = 0.85 \begin {gather*} -\frac {4}{x} + \frac {3}{2 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-4/x + 3/2/x^2

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Mupad [B]
time = 0.03, size = 10, normalized size = 0.77 \begin {gather*} -\frac {8\,x-3}{2\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4/x^2 - 3/x^3,x)

[Out]

-(8*x - 3)/(2*x^2)

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