Question

Integrate:

Answer 1

\[\LARGE \int~\sqrt{x^2+1}~dx\]

Answer 2

try this
x = tan(θ)

Answer 3

Change it to \(\Large \int~\sqrt{tan^2u+1}du\)?
Then use the trig identity?

Answer 4

Whoops, \(*sec^2u\) on the outside.

Answer 5

that gives u sec^3 and u can spend an hour or two integrating it..

if you're allowed to use tables, u may pick it directly from the table (7th integral)
http://integral-table.com/downloads/single-page-integral-table.pdf

Answer 6

who allows the table x-(

Answer 7

ikr... :)

Answer 8

well
i would say , does this work ?

Answer 9

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

\[\sqrt{x^2+1} = \sqrt{\tan^2 \theta +1}\]

\[\int\limits \sec^3 \theta d \theta \] and now you can use a reduction formula.

Answer 10

or an hyperbolic substitution again gives u the answer fast

Answer 11

ahem there is a direct formula tho:
http://prntscr.com/3qfghx