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evaluate the following integral ∫ cos 2x / (cos x + sin x)^2 dx

evaluate the following integral
∫ cos 2x / (cos x + sin x)^2 dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello student,
Please find the answer to your question below

I = \int \frac{cos2x}{(cosx+sinx)^2}dx
I = \int \frac{cos2x}{(cos^{2}x+sin^{2}x+2sinxcosx)}dx
I = \int \frac{cos2x}{(1+sin2x)}dx
1+sin2x = t
2cos2xdx = dt
I = \frac{1}{2}\int \frac{dt}{t}
I = \frac{1}{2}log(t) + c
I = \frac{1}{2}log(1+sin2x) + c

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