Evaluate the following integral:∫x2x3−5−−−−−√dx

The integral you provided is a bit unclear, but I'm assuming you're asking for the integral of x^2/sqrt(x^3 - 5). Here's how you can solve it:

Step 1: Rewrite the integral The integral ∫x^2/sqrt(x^3 - 5) dx can be rewritten as ∫x^2*(x^3 - 5)^(-1/2) dx.

Step 2: Use substitution Let u = x^3 - 5. Then du = 3x^2 dx. We can rewrite x^2 dx as (1/3)du. So the integral becomes (1/3)∫u^(-1/2) du.

Step 3: Use the power rule The power rule states that ∫x^n dx = (1/(n+1))x^(n+1) + C. Applying this rule to our integral gives us (1/3)*2u^(1/2) + C = (2/3)(x^3 - 5)^(1/2) + C.

So, the integral ∫x^2/sqrt(x^3 - 5) dx = (2/3)(x^3 - 5)^(1/2) + C.