# Evaluate the following integral:

Let us assume

Adding – 1 and + 1

Let

Thus I = I1 – I2 …….equation 1

Solving for I1

since

I1 = [tan – 1(∞) – tan – 1(0)]

I1 = π/2 ……….equation 2

Solving for I2

Let .....…..equation 3

a + b = 0; a + c = 1; b + c = 0

solving we get

a = c = 1/2

b = – 1/2

substituting the values in equation 3

Thus substituting the values in I2, thus

Solving :

Let 1 + x2 = y

2xdx = dy

For x = ∞

y = ∞

For x = 0

y = 0

substituting values

Thus

……….equation 4

Substituting values equation 2 and equation 4 in equation 1

Thus

I = I1 – I2

I = π/2 – π/4

I = π/4

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