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evaluate the following integral ∫ (2 cos x – 3 sin x) / (6 cos x + 4 sin x) dx

evaluate the following integral
∫ (2 cos x – 3 sin x) / (6 cos x + 4 sin x) dx

Grade:12

1 Answers

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

I = \int \frac{2cosx-3sinx}{6cosx+4sinx}dx
6cosx + 4sinx = t
(-6sinx+4cosx)dx = dt
2(-3sinx+2cosx)dx = dt
I = \int \frac{dt}{2t}
I = \frac{logt}{2} + c
I = \frac{log(4sinx+6cosx)}{2} + c

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