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

Find the number of roots of the equation log_(e)(1+x)-(tan^(-1)x)/(1+x)=0

Find the number of roots of the equation log_(e)(1+x)-(tan^(-1)x)/(1+x)=0

Find the number of roots of the equation log_(e)(1+x)-(tan^(-1)x)/(1+x)=0

The value of e^(log_(e)){tan(2tan^(-1)((1)/(5))-(pi)/(4))}

Evaluate: (i) int((sin(log x))/(x)dx (ii) int(e^(m)tan(-1)x)/(1+x^(2))dx

y=log_(e)(tan^(-1)sqrt(1+x^(2))) then (dy)/(dx) is

int(x^(3)-1)/(x^(3)+x)dx is equal to a) x-log_(e)|x|+log_(e)(x^(2)+1)-tan^(-1)x+C b) x-log_(e)|x|+1/2log_(e)(x^(2)+1)-tan^(-1)x+C c) x+log_(e)|x|+1/2log_(e)(x^(2)+1)+tan^(-1)x+C d)None of these

If y=tan^(-1){((log)_e(e//x^2))/((log)_e(e x^2))}+tan^(-1)((3+2\ (log)_e x)/(1-6\ (log)_e x)) , then (d^2y)/(dx^2)= (a) 2 (b) 1 (c) 0 (d) -1

If y=tan^(-1)[(log(e//x^(3)))/(log(ex^(3)))]+tan^(-1)[(log(e^(4)x^(3)))/(log(e//x^(12)))]," then "(d^(2)y)/(dx^(2))=