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

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

intsqrt(x^2-a^2)dx=(x)/(2)sqrt(x^2-a^2)-(a^2)/(2) log |x+sqrt(x^2-a^2)|+c

Prove that int frac{1}{sqrt (x^2 - a^2)} dx = log (x+ sqrt (x^2 -a^2)) + c

int frac {x+1}{x+2} dx =............ A) x+2 - log(x+2) + c B) sqrt (x^2 + 3x +2) -(1/2) log x + (3/2) + sqrt (x^2 + 3x +2) + c C) sqrt (x^2 + 3x +2) +(1/2) log x + (3/2) + sqrt (x^2 + 3x +2) + c D) sqrt (x^2 + 3x +2) -(1/2) log x + (3/2) - sqrt (x^2 + 3x +2) + c

prove that : int sqrt(x^2+a^2) dx = x/2sqrt(x^2+a^2)+a^2/2log|x+sqrt(x^2+a^2)| +c

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

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

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

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