Question

pls can someone help me with this;
Determine the following integrals by using trigonometric substitution explicitly indefinite integral 10/x^2+9dx

Answer 1

\(\Large\int{\frac{10}{x^2}+9dx}\) or \(\Large\int{\frac{10}{x^2+9}dx}~~?\)

Answer 2

@thomaster, since we're using a trig sub here, it's likely the second.

Answer 3

@SithsAndGiggles hehe english math terms are not my best point :P

Answer 4

ya, the second one

Answer 5

Let \(x=3\tan u\). Then replace \(dx\) with an expression containing \(du\), and the rest should follow through nicely.

Answer 6

got it? friend

Answer 7

na, i'm kinda stuck at the part where i supposed to substitute. should i substitute 3tanu where x^2 is?

Answer 8

nope, it is let x = 3tan u
x^2 = 9tan^2 u
+9 both sides x^2 +9 = 9tan^2 u + 9 = 9(tan^2 u +1) = 9 sec^2 u

Answer 9

oh ok, just got it!

Answer 10

good

Answer 11

my answer is 10/3u+c.

Answer 12

don't forget change the limits

Answer 13

right?

Answer 14

ah, ok. thnx a lot

Answer 15

I don't know, let me try.

Answer 16

oh, you don't have limits, sorry,

Answer 17

but it not that result, you have trig on the result

Answer 18

\[\frac{10}{9sec^2 u}= \frac {10cos^2u}{9}\]

Answer 19

and it's quite easy to take integral

Answer 20

got what I mean?

Answer 21

ya :)

Answer 22

ok, good

Answer 23

but i think u mean sec^2u instead of cos ^2u

Answer 24

nope, \[sec u = \frac{1}{cos u}---> \frac{1}{sec u} = cos u\]

Answer 25

right?