Question

∫√x-1/ x√x+1 dx is equal to

Answer 1

To solve the integral ∫(√(x-1))/(x√(x+1)) dx, we can simplify the expression and then apply the inverse power rule for integrals.

Step-by-step explanation:

To solve the integral ∫(√(x-1))/(x√(x+1)) dx, we can simplify the expression first:

Let's rewrite the integrand as (√(x-1))/(x^(3/2)√(x+1)).

We notice that the derivative of (x+1) is dx, so we can make the substitution u = x+1.

Substituting u = x+1, we have: ∫(√(u-2))/(u^(3/2) dx.

Now, let's rewrite the expression as (√(u-2))/((u-1)^(3/2)).

We can now apply the inverse power rule for integrals to solve the integral: ∫(u)^(-3/2)(√(u-2)) du.