3.61.98 \(\int \frac {-3-3 \log (240)}{x^2} \, dx\)

Optimal. Leaf size=16 \[ \frac {3 (2+2 x) (1+\log (240))}{2 x} \]

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Rubi [A]  time = 0.01, antiderivative size = 9, normalized size of antiderivative = 0.56, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 30} \begin {gather*} \frac {3 (1+\log (240))}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-3 - 3*Log[240])/x^2,x]

[Out]

(3*(1 + Log[240]))/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 ((3 (1+\log (240))) \int \frac {1}{x^2} \, dx\right )\\ &=\frac {3 (1+\log (240))}{x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.56 \begin {gather*} \frac {3 (1+\log (240))}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-3 - 3*Log[240])/x^2,x]

[Out]

(3*(1 + Log[240]))/x

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fricas [A]  time = 0.71, size = 9, normalized size = 0.56 \begin {gather*} \frac {3 \, {\left (\log \left (240\right ) + 1\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*log(240)-3)/x^2,x, algorithm="fricas")

[Out]

3*(log(240) + 1)/x

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giac [A]  time = 0.13, size = 9, normalized size = 0.56 \begin {gather*} \frac {3 \, {\left (\log \left (240\right ) + 1\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*log(240)-3)/x^2,x, algorithm="giac")

[Out]

3*(log(240) + 1)/x

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maple [A]  time = 0.05, size = 10, normalized size = 0.62

method	result	size
gosper	\(\frac {3 \ln \left (240\right )+3}{x}\)	\(10\)
norman	\(\frac {3 \ln \left (240\right )+3}{x}\)	\(11\)
default	\(-\frac {-3 \ln \left (240\right )-3}{x}\)	\(12\)
risch	\(\frac {12 \ln \relax (2)}{x}+\frac {3 \ln \relax (3)}{x}+\frac {3 \ln \relax (5)}{x}+\frac {3}{x}\)	\(28\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-3*ln(240)-3)/x^2,x,method=_RETURNVERBOSE)

[Out]

3*(ln(240)+1)/x

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maxima [A]  time = 0.34, size = 9, normalized size = 0.56 \begin {gather*} \frac {3 \, {\left (\log \left (240\right ) + 1\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*log(240)-3)/x^2,x, algorithm="maxima")

[Out]

3*(log(240) + 1)/x

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mupad [B]  time = 0.04, size = 10, normalized size = 0.62 \begin {gather*} \frac {3\,\ln \left (240\right )+3}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(3*log(240) + 3)/x^2,x)

[Out]

(3*log(240) + 3)/x

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sympy [A]  time = 0.05, size = 10, normalized size = 0.62 \begin {gather*} - \frac {- 3 \log {\left (240 \right )} - 3}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*ln(240)-3)/x**2,x)

[Out]

-(-3*log(240) - 3)/x

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