Learn how to solve polynomial long division problems step by step online. Find the integral 2int((x^2+1)^(1/2))dx. We can solve the integral 2\int\sqrt{x^2+1}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get. Applying the trigonometric identity: 1+\tan\left(\theta \right)^2 = \sec\left(\theta \right)^2.

Find the integral 2int((x^2+1)^(1/2))dx