`int_(1)^4(3/2 sqrt(x) - 4/x^2) dx`

int sqrt(3-4x^(2))dx

int sqrt(1-4x^(2))dx

int_(1)^(3)(1)/(sqrt(4x-x^(2)-3))dx=

I_(1)=int_(1)^(2)sqrt(sin(3x-x^(2)-2))dx and I_(2)=int_(1)^(3)sqrt(sin((4x-x^(2)-3)/(4)))dx then the value of 2I_(1)-I_(2) is

int_(-4)^(-2)(sqrt(x^(2)-4))/(4)dx

int(1)/(sqrt(4x^(2)-x+4))dx

int_(2)^(4)(sqrt(x^(2)-4))/(4)dx is equal to

int_(-2)^(2)(x-3)sqrt(4-x^(2))dx

int_(0)^(2)x^(2)sqrt(4-x^(2))dx=

(1) int_(-1)^(0)(x)/(sqrt(x^(2)+4))*dx