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Integrate the following and kindly please simplify itsinx + cosx / 3 + sin2x

Integrate the following and kindly please simplify itsinx + cosx / 3 + sin2x

Grade:12

1 Answers

Arun
25750 Points
6 years ago
First take the denominator
3 + sin2x
= 4-1 + sin 2x
= 4 - (1- sin 2x)
= 4 - ( sinx- cos x)²
 
Now your question will become
(Sinx + cosx)/[2² - (sinx- cosx)²]
 
Assume sinx - cos x = t
Hence (cos x + sinx ) dx = dt
Now question is in the form
dt/2² - t²
Now I think you would be able to solve this

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