" 2."(i)quad 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

Integration of (1)/(1+((log)_(e)x)^(2)) with respect to (log)_(e)x is ((tan^(-1)((log)_(e)x))/(x)+C(b)tan^(-1)((log)_(e)x)+C(c)(tan^(-1)x)/(x)+C(d) none of these

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

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)(e/x^(2)))/((log_(e)(ex^(2)))}+tan^(-1)((3+2(log)_(e)x)/(1-6(log)_(e)x)), then (d^(2)y)/(dx^(2))=(a)2(b)1(c)0(d)-1

If quad y=tan^(-1){(log_(e)((e)/(x^(2))))/(log_(e)(ex^(2)))}+tan^(-1)((3+2log_(e)x)/(1-6log_(e)x)), then (d^(2)y)/(dx^(2))=