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

int_(1)^(2)x sqrt(3x-2)dx

int(1)/(5^(2)+(sqrt(3)x)^(2))dx

int(1)/(sqrt(1-(3x+2)^(2)))dx

Evaluate the following : (i) int(x+(1)/(x))^(3//2)((x^(2)-1)/(x^(2)))dx " (ii) " int(sqrt(2+logx))/(x)dx (iii) int((sin^(-1)x)^(3))/(sqrt(1-x^(2)))dx " (iv) " int(cotx)/(sqrt(sinx))dx

int_(1)^((4sqrt(3))/(5)-1)(x+2)/(sqrt(x^(2)+2x-3))dx equal to

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(dx)/(sqrt((a^(2)-x^(2))^(3)))

Prove that: int_(-a)^(a) x^(3) sqrt(a^(2) -x^(2) ) dx=0

int_(-1)^((1)/(2))(e^(x)(2-x^(2))dx)/((1-x)sqrt(1-x^(2))) is equal to (sqrt(e))/(2)(sqrt(3)+1) (b) (sqrt(3e))/(2)sqrt(3e)(d)sqrt((e)/(3))