Question

Integrate 2v/v^2-1.dv

Answer 1

$\implies\displaystyle \int \dfrac{2v}{ {v}^{2} - 1} \: dv$

We will Integer the above expression using substitution method.

$let \: \: ( {v}^{2} - 1) = t$

$2v \: dv = dt$

$\implies\displaystyle \int \dfrac{dt}{ t} \:$

$\implies\displaystyle log(t) + c$

now put t = v²-1

$\implies\displaystyle log( {v}^{2} - 1 ) + c$

Answer :

$\displaystyle log( {v}^{2} - 1 ) + c$

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∫ cos x dx = sin x + C

∫ sec2 dx = tan x + C

∫ csc2 dx = -cot x + C

∫ sec x (tan x) dx = sec x + C

∫ csc x ( cot x) dx = – csc x + C

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