" 1.(i) "x^(2)tan^(-1)x

" (i) "int(e^(tan^(-1)x)dx)/((1+x^(2))

int (e^(x) (x^(2) tan^(-1) x + tan^(-1) x + 1))/( x^(2) + 1) dx is

" (i) "tan( 1/2(tan^(-1)x+tan^(-1)(1/x)))=1

The values of x satisfying the inequality [tan^(-1)x]^(2)-[tan^(-1)x]-2<=0 is (1.] denotes G.I.F.)

(i) int(1)/((1+x^(2))tan ^(-1) x )dx " "(ii) int(e^(tan^(-1)x))/(1+x^(2))dx

(i) int(1)/((1+x^(2))tan ^(-1) x )dx " "(ii) int(e^(tan^(-1)x))/(1+x^(2))dx

Solve : (i)" "tan^(-1). x/2 +tan^(-1). x/3 = pi/4 , sqrt(6) gt x gt 0 (ii)" "sin(sin^(-1) . 1/5+cos^(-1)x)=1

2tan(tan^(-1)(x)+tan^(-1)(x^(3))), where x in R-{-1,1} is equal to (2x)/(1-x^(2))t(2tan^(-1)x)tan(cot^(-1)(-x)-cot^(-1)(x))tan(2cot^(-1)x)

Evaluate: (i) sin(tan^(-1)x+(tan^(-1)1)/(x)) for x>0( ii) cot(tan^(-1)a+cot^(-1)a)