Evaluate

Let I =

Multiplying by 5 in numerator and denominator

⇒ I =

⇒ I =

⇒ I = I_{1} + I_{2}

I_{1} =

Let 5x^{2} + 1 = t ….(i)

d(5x^{2} + 1) = dt

10x dx = dt …..(ii)

When x = 0; t = 5 × 0^{2} + 1 = 1

When x = 1; t = 5 × 1^{2} + 1 = 6

Substituting (i) and (ii) in I_{1}

I_{1} = *[**]*

I_{1} =

I_{1} =

I_{2} = *[**]*

I_{2} =

I_{2} = 3/√5 tan^{-1}5

∵ I = I_{1} + I_{2}

∴ I = 1/5 log 6 + 3/√5 tan^{-1}5

∴ = 1/5 log 6 + 3/√5 tan^{-1}5

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