" (i) "int(dx)/(x^(2)-a^(2))=(1)/(2a)log|(x-a)/(x+a)|+C

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

If int (dx)/(a^(2)-x^(2))=(1)/(2a) log |f(x)|+c then f(x) is-

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

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

int(1)/(x(log x)^(2))dx

" "int(log x)/((1+x)^(2))dx

int(x ln x)/((x^(2)-1)^((3)/(2)))dx

If int(dx)/(x^(4)+x^(2))=(A)/(x^(2))+(B)/(x)+ln|(x)/(x+1)|+C then

int(x log(x+1)^(2)dx)