Question

Find ∫x√(1-x)dx
please someone help me​ ​

Answer 1

⅖ (1 − x)^(5/2) − ⅔ (1 − x)^(3/2) + C

Explanation:

∫ x√(1 − x) dx

If u = 1 − x, then x = 1 − u, and dx = -du.

∫ (1 − u) √u (-du)

∫ (u − 1) √u du

∫ (u^(3/2) − u^(1/2)) du

⅖ u^(5/2) − ⅔ u^(3/2) + C

⅖ (1 − x)^(5/2) − ⅔ (1 − x)^(3/2) + C