Evaluate the given equation by integration. ∫(√tan x + √cot x) dx

Evaluate the given equation by integration.

∫(√tan x + √cot x) dx

Expert Solution

∫(√tan x + √cot x) dx = ∫(√(sin x/cos x) + √(cos x/sin x)dx

= √2 ∫(sin x + cos x)/√sin 2x dx

Put sin x – cos x = t

=> (cos x + sin x) dx = dt

Also (sin x – cos x)² = t²

1 – sin 2x = t²

=> sin 2x = 1-t²

I = √2 ∫ dt/ √(1-t²)

= √2 sin-¹ t + C

= √2 sin-¹(sin x – cos x) + C

Value of ∫(√tan x + √cot x) dx = √2 sin-¹(sin x – cos x) + C

Nikhil Thakur answered 2 years ago

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