" (iv) "(1)/(1+9x^(2))quad " (v) "()/(sqrt(1))

Integrate the following with respect to x. (i) 1/(1 + (2x)^2) " " (ii) 1/(sqrt(1 - (9x)^2)) " " (iii) 1/(sqrt(1 - 25x^2)) .

int (1)/(sqrt(4-9x^(2))dx=

int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k _(1)) ( sqrt(1-9x ^(2))+ (cos ^(-1) 3x )^(k_(2)))+c, then k _(1) ^(2)+k_(2)^(2)= (where C is an arbitrary constnat. )

int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k _(1)) ( sqrt(1-9x ^(2))+ (cos ^(-1) 3x )^(k_(2)))+c, then k _(1) ^(2)+k_(2)^(2)= (where C is an arbitrary constnat. )

If for x(0,(1)/(4)), the derivative of tan^(-1)((6x sqrt(x))/(1-9x^(3))) is sqrt(x)g(x), then g(x) equals: (1)(3x)/(1-9x^(3))(2)(3)/(1+9x^(3))(3)(9)/(1+9x^(3)) (4) (3x sqrt(x))/(1-9x^(3))

(v)int e^x(sqrt(1-x^(2))-(x)/(sqrt(1-x^2))dx)

int((9)/(sqrt(1-x^(2)))+(5)/(sqrt(1+x^(2))))dx

Integrate (8)/(sqrt(1-(4x)^(2)))+(27)/(sqrt(1-9x^(2)))-(15)/(1+25x^(2)) with respect to x .