Question

Integrate (sqrt(1 + x^2)/x)

Answer 1

\[x = \tan \theta dx = \sec^2 \theta \]

Answer 2

I think I need a simpler route with the trig substitution.... the way I tried was lasting almost two pages....

Answer 3

yes, that substitution is correct, so what did u get in terms of theta ?

Answer 4

It's the substituting it into the equation, then simplifying that I experienced trouble with.

Answer 5

1+tan^2 theta = ?
sec theta* coas theta = ?

Answer 6

*cos

Answer 7

u get sec theta * sec^2 theta / tan theta , right ?

Answer 8

yeah

Answer 9

so what is sec theta / tan theta ??
and write sec^2 theta as 1+ tan^2 theta

Answer 10

u will get , csc t (1+sec^2 t)
= csc t +csc t .sec^2 t
=csc t+ tan t sec t
integrate these seperately, these are standard integrals.
then resubstitute for t