Learn how to solve two-variable linear equations problems step by step online. Find the integral int(-1/(y(y^2+1)^(1/2)))dy. We can solve the integral \int\frac{-1}{y\sqrt{y^2+1}}dy by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dy, we need to find the derivative of y. We need to calculate dy, 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 int(-1/(y(y^2+1)^(1/2)))dy