int sin^(-1)((2x+2)/(sqrt(4x^(2)+9x^(2)+13)))dx

Evaluate: int sin^(-1)((2x+2)/(sqrt(4x^(2)+8x+13)))dx

∫sin^(-1)((2x+2)/(sqrt(4x^(2)+8x+13))) dx is,

If int sin^-1 ((2x + 2)/sqrt(4x^2 + 8x + 13)) dx = (x + 1) tan^-1 ((2x+2)/3) + lambda In (4x^2 + 8x + 13) + c , then the value of -4lambda must be

int(2sin^(-1)x)/(sqrt(1-x^(2)))dx

int(dx)/(sqrt(4x^(2)-9))

int (1)/((x^(2)+9)sqrt(x^(2)-9))dx=

int(dx)/(sqrt(9-4x^(2)))

int x sqrt((9-x^(2))/(9+x^(2)))dx=

int(2x+9)/(sqrt(x^(2)+x+1))dx