Utilizes the denominator for our substitution, Mathematics

Assignment Help:

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,

1237_Substitution 4.png

∫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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