Easy integration (1 Viewer)

[erm]

for some reason (god knows) i can't integrate the following:

1/sqrt(1+x^2)

any help at all would be really appreciated!

 

[hollyy.]

for some reason (god knows) i can't integrate the following:

1/sqrt(1+x^2)

any help at all would be really appreciated!

you sure it's not a minus instead of a plus?
if not, i don't know.

 

[webby234]

for some reason (god knows) i can't integrate the following:

1/sqrt(1+x^2)

any help at all would be really appreciated!

Try a trigonometric substitution?
x = tanu
dx = sec²u du

sec²/sqrt(1+tan²u)
= sec²u/secu
= sec u

You can intergrate that in the usual way (multiply by (secu+tanu)/(secu+tanu))

EDIT: Sorry, thought this was extension 2.
Yeah that question is beyond the scope of extension 1.
EDIT2: Actually, is that not on the standard integrals sheet?

 

[erm]

you sure it's not a minus instead of a plus?
if not, i don't know.

that's what i thought, but apparently not.

the answer (from terry lee textbook) goes:

dt/dx = 1/sqrt(1+x^2)

t = ln(x+sqrt(x^2 +1)) + C

how did they get to that?

 

[erm]

Try a trigonometric substitution?
x = tanu
dx = sec²u du

sec²/sqrt(1+tan²u)
= sec²u/secu
= sec u

You can intergrate that in the usual way (multiply by (secu+tanu)/(secu+tanu))

EDIT: Sorry, thought this was extension 2.
Yeah that question is beyond the scope of extension 1.
EDIT2: Actually, is that not on the standard integrals sheet?

Just checked and yes, you are correct! It's weird i've never seen that before...

so could someone show me the working or do i just accept this as a standard form that i must memorise?

 

[shinn]

one of the formula in the standard integral sheet

 

[u-borat]

thats a rare question...when u get it, just use the standard integral...u won't find it much in exams imo.

 

[erm]

thats a rare question...when u get it, just use the standard integral...u won't find it much in exams imo.

cheers and thank you.

 

[webby234]

Just checked and yes, you are correct! It's weird i've never seen that before...

so could someone show me the working or do i just accept this as a standard form that i must memorise?

You need four unit stuff.

 

[erm]

You need four unit stuff.

ah ok. I wouldn't want to venture there.

 

[u-borat]

if they gave you the substitution, couldn't that question potentially be in a 3unit exam?

 

[webby234]

if they gave you the substitution, couldn't that question potentially be in a 3unit exam?

I think you have to integrate sec x, which is difficult unless you see the magic

You need to see that:

secu =
secu (secu + tanu)
-----------------------
secu + tanu

which is of the form (after expanding) of f'(x)/f(x) so it's log (secu + tanu) then you need to sub back in tanu = x
and secu = rt(1 + x²)
(as sec²u = 1 + tan²u) = 1 + x²)

So that's difficult unless you see the trick.