3.32.61 \(\int -\frac {8}{5 x^2} \, dx\) [3161]

Optimal. Leaf size=27 \[ \frac {4}{5} \left (1+\frac {2}{x}+3 \log (2)-\log \left (\frac {\log (3)}{5 e^4}\right )\right ) \]

[Out]

4/5+8/5/x-4/5*ln(1/5*ln(3)/exp(4))+12/5*ln(2)

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Rubi [A]
time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.26, 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 {8}{5 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-8/(5*x^2),x]

[Out]

8/(5*x)

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 {8}{5} \int \frac {1}{x^2} \, dx\right )\\ &=\frac {8}{5 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 7, normalized size = 0.26 \begin {gather*} \frac {8}{5 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-8/(5*x^2),x]

[Out]

8/(5*x)

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Maple [A]
time = 0.01, size = 6, normalized size = 0.22

method	result	size
gosper	\(\frac {8}{5 x}\)	\(6\)
default	\(\frac {8}{5 x}\)	\(6\)
norman	\(\frac {8}{5 x}\)	\(6\)
risch	\(\frac {8}{5 x}\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-8/5/x^2,x,method=_RETURNVERBOSE)

[Out]

8/5/x

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Maxima [A]
time = 0.26, size = 5, normalized size = 0.19 \begin {gather*} \frac {8}{5 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8/5/x^2,x, algorithm="maxima")

[Out]

8/5/x

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Fricas [A]
time = 0.51, size = 5, normalized size = 0.19 \begin {gather*} \frac {8}{5 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8/5/x^2,x, algorithm="fricas")

[Out]

8/5/x

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Sympy [A]
time = 0.01, size = 3, normalized size = 0.11 \begin {gather*} \frac {8}{5 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8/5/x**2,x)

[Out]

8/(5*x)

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Giac [A]
time = 0.40, size = 5, normalized size = 0.19 \begin {gather*} \frac {8}{5 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8/5/x^2,x, algorithm="giac")

[Out]

8/5/x

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Mupad [B]
time = 0.02, size = 5, normalized size = 0.19 \begin {gather*} \frac {8}{5\,x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-8/(5*x^2),x)

[Out]

8/(5*x)

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