integrate 1 / sqrt (25 - 16x^2) dx

The main formula is integr U^p du = (1/1+p) U^p+1

let be U = (25 - 16x^2) ^-1/2,

1/sqrt (25 - 16x^2) = (25 - 16x^2) ^-1/2

du = - 1/2) (-32x) (25 - 16x^2) ^-1/2dx

integ du/-1/2) (-32x) = integ (25 - 16x^2) ^-1/2dx

nteg du/16x) = 1/16xu+c=integ (25 - 16x^2) ^-1/2dx

finally

integ 1 / sqrt (25 - 16x^2) dx = 1/16xu+c = (1/16x) ((25 - 16x^2) ^-1/2) + c