3.60.27 \(\int -\frac {4}{5 x^3} \, dx\)

Optimal. Leaf size=13 \[ 100-\frac {2}{5} \left (2-\frac {1}{x^2}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.54, number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 30} \begin {gather*} \frac {2}{5 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-4/(5*x^3),x]

[Out]

2/(5*x^2)

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left (\frac {4}{5} \int \frac {1}{x^3} \, dx\right )\\ &=\frac {2}{5 x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.54 \begin {gather*} \frac {2}{5 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-4/(5*x^3),x]

[Out]

2/(5*x^2)

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fricas [A]  time = 0.56, size = 5, normalized size = 0.38 \begin {gather*} \frac {2}{5 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/5/x^3,x, algorithm="fricas")

[Out]

2/5/x^2

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giac [A]  time = 0.12, size = 5, normalized size = 0.38 \begin {gather*} \frac {2}{5 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/5/x^3,x, algorithm="giac")

[Out]

2/5/x^2

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maple [A]  time = 0.01, size = 6, normalized size = 0.46

method	result	size
gosper	\(\frac {2}{5 x^{2}}\)	\(6\)
default	\(\frac {2}{5 x^{2}}\)	\(6\)
norman	\(\frac {2}{5 x^{2}}\)	\(6\)
risch	\(\frac {2}{5 x^{2}}\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-4/5/x^3,x,method=_RETURNVERBOSE)

[Out]

2/5/x^2

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maxima [A]  time = 0.35, size = 5, normalized size = 0.38 \begin {gather*} \frac {2}{5 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/5/x^3,x, algorithm="maxima")

[Out]

2/5/x^2

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mupad [B]  time = 0.03, size = 5, normalized size = 0.38 \begin {gather*} \frac {2}{5\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-4/(5*x^3),x)

[Out]

2/(5*x^2)

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sympy [A]  time = 0.05, size = 5, normalized size = 0.38 \begin {gather*} \frac {2}{5 x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/5/x**3,x)

[Out]

2/(5*x**2)

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