Evaluate

Let I =

Multiplying by 5 in numerator and denominator

⇒ I =

⇒ I =

⇒ I = I₁ + I₂

I₁ =

Let 5x² + 1 = t ….(i)

d(5x² + 1) = dt

10x dx = dt …..(ii)

When x = 0; t = 5 × 0² + 1 = 1

When x = 1; t = 5 × 1² + 1 = 6

Substituting (i) and (ii) in I₁

I₁ = []

I₁ =

I₁ =

I₂ = []

I₂ =

I₂ = 3/√5 tan^-15

∵ I = I₁ + I₂

∴ I = 1/5 log 6 + 3/√5 tan^-15

∴ = 1/5 log 6 + 3/√5 tan^-15