Question

how to prove ????
integral(1/sqrt(a^2+x^2), x)=ln(abs(sqrt(x^2+a^2)+x))

Answer 1

(sinh(x/a))^-1 to this answer

Answer 2

try let x = a tan (theta)
dx = ....

Answer 3

a sec^2 (theta)

Answer 4

yes, right ... so it can be :
int (a sec^2 (theta)/a sec(theta)) d(theta) right ? simplify again,
int sec(theta) d(theta) , agree ?

Answer 5

ln (abs) tanx+sec x

Answer 6

ok i got ln ((x+(sqrt)x^2+a^2)) /a)+c