3.38.33 \(\int \frac {75}{-124+75 x} \, dx\)

Optimal. Leaf size=8 \[ \log \left (\frac {124}{25}-3 x\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 6, normalized size of antiderivative = 0.75, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 31} \begin {gather*} \log (124-75 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[75/(-124 + 75*x),x]

[Out]

Log[124 - 75*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} &=75 \int \frac {1}{-124+75 x} \, dx\\ &=\log (124-75 x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 6, normalized size = 0.75 \begin {gather*} \log (-124+75 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[75/(-124 + 75*x),x]

[Out]

Log[-124 + 75*x]

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fricas [A]  time = 0.87, size = 6, normalized size = 0.75 \begin {gather*} \log \left (75 \, x - 124\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(75/(75*x-124),x, algorithm="fricas")

[Out]

log(75*x - 124)

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giac [A]  time = 0.16, size = 7, normalized size = 0.88 \begin {gather*} \log \left ({\left | 75 \, x - 124 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(75/(75*x-124),x, algorithm="giac")

[Out]

log(abs(75*x - 124))

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maple [A]  time = 0.09, size = 7, normalized size = 0.88

method	result	size
default	\(\ln \left (75 x -124\right )\)	\(7\)
norman	\(\ln \left (75 x -124\right )\)	\(7\)
meijerg	\(\ln \left (1-\frac {75 x}{124}\right )\)	\(7\)
risch	\(\ln \left (75 x -124\right )\)	\(7\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(75/(75*x-124),x,method=_RETURNVERBOSE)

[Out]

ln(75*x-124)

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maxima [A]  time = 0.37, size = 6, normalized size = 0.75 \begin {gather*} \log \left (75 \, x - 124\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(75/(75*x-124),x, algorithm="maxima")

[Out]

log(75*x - 124)

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mupad [B]  time = 0.07, size = 4, normalized size = 0.50 \begin {gather*} \ln \left (x-\frac {124}{75}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(75/(75*x - 124),x)

[Out]

log(x - 124/75)

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sympy [A]  time = 0.05, size = 5, normalized size = 0.62 \begin {gather*} \log {\left (75 x - 124 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(75/(75*x-124),x)

[Out]

log(75*x - 124)

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