3.1908 \(\int (-\frac{3}{x^3}+\frac{4}{x^2}) \, dx\)

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 = 0.0019179, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{3}{2 x^2}-\frac{4}{x} \]

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*}

Mathematica [A]  time = 0.0013716, size = 13, normalized size = 1. \[ \frac{3}{2 x^2}-\frac{4}{x} \]

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., size = 12, normalized size = 0.9 \begin{align*}{\frac{3}{2\,{x}^{2}}}-4\,{x}^{-1} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/2/x^2-4/x

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Maxima [A]  time = 0.989355, size = 15, normalized size = 1.15 \begin{align*} -\frac{4}{x} + \frac{3}{2 \, x^{2}} \end{align*}

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 = 1.82569, size = 27, normalized size = 2.08 \begin{align*} -\frac{8 \, x - 3}{2 \, x^{2}} \end{align*}

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 = 0.074432, size = 10, normalized size = 0.77 \begin{align*} - \frac{8 x - 3}{2 x^{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(8*x - 3)/(2*x**2)

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Giac [A]  time = 1.05104, size = 15, normalized size = 1.15 \begin{align*} -\frac{4}{x} + \frac{3}{2 \, x^{2}} \end{align*}

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