Question

integrate x/sqroot of x^4-1

Answer 1

nasty integral.

Answer 2

1/2 cosh^-1(x^2)

Answer 3

thanks dave,,, but i want to know how to do it

Answer 4

he made the substitution x = cosh(u)

Answer 5

step by step

Answer 6

sorry. he made the substitution x^2 = cosh(u)

Answer 7

hence 2xdx = sinh(u)du, so the integral reduces to:

int(1/2*sinh(u)du/sqrt((cosh(u))^2 - 1))

= int(1/2*sinh(u)du/sinh(u))

= int(1/2 * du)

= 1/2 * u + C

= 1/2 * arccos(x^2) + C

Answer 8

\[u=x^2\]
The equation now becomes \[1/2\int\limits1/\sqrt(u^2 -1)\]
which is the derivative of arcosh(u)
Plug the 1/2 back in and switch the u for x^2 and you get
\[1/2\cosh^{-1} (x^2)\]