Question

Use Trig Substitution to solve the integral of ((dt)/(t^2)(square root of 1+t^2))

Answer 1

no more partial fractions?

Answer 2

nope! im good with partial fractions! i can do those in my sleep:)

Answer 3

my professor taught Trig Substitution with just letters....no numbers in the examples or anything so I am so confused its crazy

Answer 4

okay... just a sec.

Answer 5

thank you:)

Answer 6

lol
partial fractions for days

Answer 7

@pgpilot326 can probably do this better, but if i remember correctly when you see
\[\sqrt{1+x^2}\] you use \(x=\tan(\theta)\)

Answer 8

because
\[1+\tan^2(\theta)=\sec^2(\theta)\]

Answer 9

yup ive got that far! lol

Answer 10

so now if x = tan theta, what's dx?

Answer 11

sec^2(theta)

Answer 12

theres a d(theta) after that sorry

Answer 13

do some trig simplification
there will be a ton of cancellation

Answer 14

\[\frac{\sec^2(\theta)}{\tan^2(\theta)sec(\theta)}\] is the first step, but tons goes

Answer 15

so then this becomes
\[\int\limits\frac{ dt }{t^{2}\sqrt{1+t^{2} }}= \int\limits\frac{ \sec ^{2} \theta d \theta }{\tan ^{2} \theta \sec \theta }\]

Answer 16

okay :) just pluggin in easy enough

Answer 17

hint: you end up with something you know the anti derivative of instantly (i think)

Answer 18

yep... just like @satellite73 said, there's cancellation. don't forget to draw the triangle used for the trig sub as you may need other things from it after integrating

Answer 19

yup ive got the triangle! :)

Answer 20

so am i able to cancel out the secants with one left in the numerator? or can i not do that?

Answer 21

yep

Answer 22

so am i just left with -csc(theta)+c

Answer 23

yes, but now back to x

Answer 24

im not sure how to go back

Answer 25

use the triangle

Answer 26

i know how to write out the triangle but im not real sure what to do with it:(

Answer 27

sorry:(

Answer 28

draw your triangle and i'll respond and show you

Answer 29

i bet it will be clear once you get it

Answer 30

csc = h/o