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Evaluate given integrals.
∫3/(5 y + 4) dy
Solution
Let's notice as well that if we take the denominator & differentiate it we get only a constant and the only thing which we have in the numerator is also a constant. It is a pretty good hint that we can utilizes the denominator for our substitution
so,
u = 5 y + 4 du = 5 dy ⇒ dy = 1/5 du
Now the integral is,
∫3/ (5 y + 4) dy = 3/5 ∫ 1/u du
= 3/5 ln |u| +c
= 3 ln |5 y + 4 |+ c
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