integrel of(1-cot^(n-2)x)dx -------------------- tanx+cotx.cot^(n-2)x integral of 3+2cosx dx ----------- (2+3cosx)^2 integral of dx ------------------ (1+x^0.5)(x-x^2)^0.5

(1+x^0.5)(x-x^2)^0.5 dx = I

let x = sin²(q)

I = 2sin²(q)cos²(q)(1+sin(q)) dq

= ((sin²(2q)/2)dq+ 2 cos²(q)(1-cos²(q))dq

= (1-cos(4(theta))) d(theta) + 2cos²(q)sin(theta) d(theta) -  2cos⁴(q)sin(theta) d(theta)

I= (theta/4) –(sin(4(theta))/16) +((2/5)cos⁵(q)) - ((2/3)cos³(q))

q = arcsin(sqrt(x))