`(1)/(2) int[(1)/(v)+(1)/(2+v)]dv=-2 int(1)/(x)dx` where `v=y/x`

int_(0)^(1)y dx where x=cos2y

int((1+v)/(1-v))dv

The value of int_(-1)^(1)sin^(-1)[x^(2)+(1)/(2)]dx+int_(-1)^(1) cos^(-1)[x^(2)-(1)/(2)]dx , where [.] denotes the greatest integer function , is

(v) int(x+2)sqrt(3x+2)dx

(V + 1) / (V (2V + 1)) dv = - (1) / (x) dx

int(1)/sqrt(1-2v^(2))dv

" (v) "int(cosx)/(1+sin x)dx

int(1+x)/(x^(2))dx+int(1-y)/(y^(2))dy

int e ^ (- (v) / (u)) dv

(i) int(1)/((1+cos2x))dx , (ii) int (1)/((1-cos2x)) dx