" 6."int(dx)/(sqrt(2ax-x^(2)))=a^(n)log x^(-1)[(x)/(a)-1]

In the equation int (dx)/sqrt(2ax - x^(2) ) = a^(2) sin ^(-1) [(x)/(a) - 1] . Find the value of n .

int ln(x+sqrt(1+x^(2)))dx

(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 log (x+sqrt(x^(2)-1))dx=

int(dx)/(sqrt(x^(2)+2x+1))=A log|x+1|+C , x!=-1

int_(0)^(1)(log x)/(sqrt(1-x^(2)))dx

" (1) "int log(x+sqrt(x^(2)-a^(2)))dx

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

int(sqrt(x^(2)+1)(log(x^(2)+1)-2log x))/(x^(4))dx