3.8.25 \(\int -\frac {80 \log (3)}{61+20 x} \, dx\)

Optimal. Leaf size=14 \[ 4 \log (3) \left (2-\log \left (\frac {61}{20}+x\right )\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.71, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 31} \begin {gather*} -4 \log (3) \log (20 x+61) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-80*Log[3])/(61 + 20*x),x]

[Out]

-4*Log[3]*Log[61 + 20*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 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left ((80 \log (3)) \int \frac {1}{61+20 x} \, dx\right )\\ &=-4 \log (3) \log (61+20 x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.71 \begin {gather*} -4 \log (3) \log (61+20 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-80*Log[3])/(61 + 20*x),x]

[Out]

-4*Log[3]*Log[61 + 20*x]

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fricas [A]  time = 1.10, size = 10, normalized size = 0.71 \begin {gather*} -4 \, \log \relax (3) \log \left (20 \, x + 61\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-80*log(3)/(20*x+61),x, algorithm="fricas")

[Out]

-4*log(3)*log(20*x + 61)

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giac [A]  time = 0.23, size = 11, normalized size = 0.79 \begin {gather*} -4 \, \log \relax (3) \log \left ({\left | 20 \, x + 61 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-80*log(3)/(20*x+61),x, algorithm="giac")

[Out]

-4*log(3)*log(abs(20*x + 61))

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maple [A]  time = 0.17, size = 11, normalized size = 0.79

method	result	size
default	\(-4 \ln \relax (3) \ln \left (20 x +61\right )\)	\(11\)
norman	\(-4 \ln \relax (3) \ln \left (20 x +61\right )\)	\(11\)
meijerg	\(-4 \ln \relax (3) \ln \left (1+\frac {20 x}{61}\right )\)	\(11\)
risch	\(-4 \ln \relax (3) \ln \left (20 x +61\right )\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-80*ln(3)/(20*x+61),x,method=_RETURNVERBOSE)

[Out]

-4*ln(3)*ln(20*x+61)

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maxima [A]  time = 0.72, size = 10, normalized size = 0.71 \begin {gather*} -4 \, \log \relax (3) \log \left (20 \, x + 61\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-80*log(3)/(20*x+61),x, algorithm="maxima")

[Out]

-4*log(3)*log(20*x + 61)

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mupad [B]  time = 0.53, size = 8, normalized size = 0.57 \begin {gather*} -4\,\ln \left (x+\frac {61}{20}\right )\,\ln \relax (3) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(80*log(3))/(20*x + 61),x)

[Out]

-4*log(x + 61/20)*log(3)

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sympy [A]  time = 0.05, size = 12, normalized size = 0.86 \begin {gather*} - 4 \log {\relax (3 )} \log {\left (20 x + 61 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-80*ln(3)/(20*x+61),x)

[Out]

-4*log(3)*log(20*x + 61)

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