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

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 = 0.00710746, 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. \[ \frac{3}{2 x^2}-\frac{4}{x} \]

Antiderivative was successfully verified.

[In]  Int[-3/x^3 + 4/x^2,x]

[Out]

3/(2*x^2) - 4/x

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Rubi in Sympy [A]  time = 1.34483, size = 8, normalized size = 0.62 \[ - \frac{4}{x} + \frac{3}{2 x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(-3/x**3+4/x**2,x)

[Out]

-4/x + 3/(2*x**2)

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Mathematica [A]  time = 0.00193142, 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 = 0.002, size = 12, normalized size = 0.9 \[{\frac{3}{2\,{x}^{2}}}-4\,{x}^{-1} \]

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 = 1.3436, size = 15, normalized size = 1.15 \[ -\frac{4}{x} + \frac{3}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(4/x^2 - 3/x^3,x, algorithm="maxima")

[Out]

-4/x + 3/2/x^2

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Fricas [A]  time = 0.192558, size = 14, normalized size = 1.08 \[ -\frac{8 \, x - 3}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(4/x^2 - 3/x^3,x, algorithm="fricas")

[Out]

-1/2*(8*x - 3)/x^2

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Sympy [A]  time = 0.069589, size = 10, normalized size = 0.77 \[ - \frac{8 x - 3}{2 x^{2}} \]

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/XCAS [A]  time = 0.271602, size = 15, normalized size = 1.15 \[ -\frac{4}{x} + \frac{3}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(4/x^2 - 3/x^3,x, algorithm="giac")

[Out]

-4/x + 3/2/x^2