" 13.1"quad " (i) "(x)/(sqrt(1-x^(2)))

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

Differentiate (i) sqrt((1+x)/(1-x)) , (ii) (x)/(sqrt(1-x^(2)))

Evaluate: (i) int(a^(x))/(sqrt(1-a^(2x)))dx (ii) int(2x)/(sqrt(1-x^(2)-x^(4)))dx

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

Integrate the following respect to x. (i) (xsin^(-1)x)/(sqrt(1-x^2)) (ii) x^5e^(x^2) (iii) tan^(-1)((8x)/(1-16x^2)) (iv) sin^(-1)((2x)/(1+x^2))

Evaluate: (i) int(a^x)/(sqrt(1-a^(2x)))\ dx (ii) int(2x)/(sqrt(1-x^2-x^4))\ dx

Let I_(1)=int_(1)^(2)(x)/(sqrt(1+x^(2)))dx and I_(2)=int_(1)^(2)(1)/(x)dx .Then

If y="tan"^(-1) (sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))) show that, (dy)/(dx)=(x)/(sqrt(1-x^(4)))

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