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

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

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

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

int(1)/(a^(2))-x^(2)dx=(1)/(2)a 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.

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

If int(1)/(x^(3)+x^(4))dx=(A)/(x^(2))+(B)/(x)+log|(x)/(x+1)|+C , then

int_(1)^(2)(log x)/(x)dx=

int log_(c)(1+x^(2))dx

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