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

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

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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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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (-\frac {3}{x^3}+\frac {4}{x^2}\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[-3/x^3 + 4/x^2,x]

[Out]

IntegrateAlgebraic[-3/x^3 + 4/x^2, x]

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fricas [A]  time = 1.23, 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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giac [A]  time = 0.90, 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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maple [A]  time = 0.00, size = 12, normalized size = 0.92 \begin {gather*} -\frac {4}{x}+\frac {3}{2 x^{2}} \end {gather*}

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 = 0.97, 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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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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sympy [A]  time = 0.08, 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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