If ∫ log t + 1 + t 2 1 + t 2 d t = 1 2 g t 2 + c , where c is a constant, then g 2 , is equal to

Step-by-step solution

Put, log t + 1 + t 2 = z ⇒ 1 t + 1 + t 2 1 + 2 t 2 1 + t 2 d t = d z ⇒ t + 1 + t 2   t + 1 + t 2   1 1 + t 2 d t = d z ⇒ 1 1 + t 2 d t = d z ∴ I = ∫ z d z = z 2 2 + c = 1 2 log t + 1 + t 2 2 + c , where c is the constant of integration. ∴ g t = log t + 1 + t 2 ⇒ g 2 = log 2 +   1 + 4 Hence, log 2 + 5 , is the answer.