Find : ∫(3sin θ - 2)cos θ/5-cos^2θ-4 sinθ

Question

Find : \(\int\frac{(3\,sin\,\theta-2)\,cos\,\theta}{5-cos^2\theta-4\,sin\,\theta}\)\(d\theta\)

Answer 1

We have,

I =  \(\int\frac{(3\,sin\,\theta-2)\,cos\,\theta}{5-cos^2\theta-4\,sin\,\theta}\)\(d\theta\) 

Let sin θ = z

Putting value of t in terms of z then z in terms of q, we get

= 3 log |sin θ - 2| - \(\frac{4}{sin\,\theta-2}+C\)