z int(1)/(a^(2)-n^(2))dn=(1)/(201)log|(a+x)/(a-r^(2))|+c

int(1)/(a^(2))-x^(2)dx=(1)/(2)a log(a+(x)/(a)-x)+c

int(1)/(x^(2)-a^(2))dx=(1)/(2)a log(x-(a)/(x)+a)+c

Prove that : int 1/(a^(2)-x^(2)) dx = 1/(2a) log |(a+x)/(a-x)|+c.

(i) int(dx)/(sqrt(a^(2)-x^(2)))=(1)/(a)sin^(-1)((x)/(a))+c (ii) int(dx)/(a^(2)+x^(2))=tan^(-1)((x)/(a))+c (iii) int(x+1)/(x^(2)+2x+1)dx=(1)/(2)log|(x^(2)+2x+1)| (iv) int(dx)/(x(x-1))dx=log|(x-1)/(x)|+c State which pair of the statement given above is true.

int(n^(4))/((n-1)(n^(2)+1))dn

I=int(sinn)/((1-cos n)^(2))dn

int_((1)/(2))^(2)(ln x)/(1+x^(2))dx

int sqrt((1-n)/(1+n))dn

int(log(x+1)-log x)/(x(x+1))dx= (A) log(x-1)log x+(1)/(2)(log x-1)^(2)-(1)/(2)(log x)^(2)+c (B) (1)/(2)(log(x+1))^(2)+(1)/(2)(log x)^(2)-log(x+1)log x+c (C) -(1)/(2)(log(x+1)^(2))-(1)/(2)(log x)^(2)+log x*log(x+1)+c (D) [log(1+(1)/(x))]^(2)+c

If int1/((x^(2)-1))log((x-1)/(x+1))dx=A[log((x-1)/(x+1))]^(2)+c , then A =