Evaluate the following Integrals:

Let


Put x = sin θ


dx = cos θ dθ (Differentiating both sides)


Also,


When x = 0, sin θ = 0 θ = 0



So, the new limits are 0 and.


Substituting this in the original integral,




Dividing numerator and denominator with cos2θ, we have




[ sec2θ = 1 + tan2θ]


Put tan θ = t


sec2θ dθ = dt (Differentiating both sides)


When θ = 0, t = tan 0 = 0



So, the new limits are 0 and.


Substituting this in the original integral,




Recall







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