Question

Evaluate the following integral : ∫ sin Φ/(√(sin^Φ + 2 cos Φ + 3)) = dΦ.

\(\int\cfrac{sin\,\phi}{\sqrt{sin^2\phi+2\,cos\,\phi+3}}\)d\(\phi\).

Answer 1

I = ∫ sin Φ/(√(sin^Φ + 2 cos Φ + 3)) = dΦ.

(\(\because\) sin²x + cos²x = 1)

Now, let cosΦ − 1 = t ⇒ − sinΦ dΦ = dt ⇒ sinΦdΦ = −dt.

Therefore,

(By putting the value of cosΦ − 1 = t )

Hence,

where C is an integral constant.