integrate!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

 x/ sqrt(a^2 - x^2 )

Answer 1

Let a^2 - x^2 = u

 => du/dx = -2x

 => -du/2 = xdx

ʃ(x / √(a^2 - x^2)) dx = ʃ -du / 2√u                                       [ Since a^2 - x^2 = u and xdx = -du/2 ]

                                   = -1/2 ʃ (1 / √u)du                            

                                   = (-1/2)(2√u) + c                            [ Since  ʃ (1 / √u)du = 2√u + c ]

                                   = - √u + c

                                   = -√ (a^2 - x^2) + c

Therefore ʃ(x / √(a^2 - x^2)) dx  = -√ (a^2 - x^2) + c