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posted by  El Duderino on 11/28/2008 4:00:45 PM  |  status: Closed  

Help! Integrals

Course Textbook Chapter Problem
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Question Details:
Evaluate the integral analitically
 
 
ò (tan (ln y)) / y dy
 
Please show all steps.
Thank you.
Tags: Calculus
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posted by roydesoto on 11/28/2008 4:25:31 PM  |  status: Live
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Response Details:
let u = ln y so du = 1/y dy

integral becomes

EDIT: fixed typo pointed out by A-Rod, please award him lifesaver credit no this, not me!

to integrate tan x, write as (sin x)/(cos x) and substitute v = cos x
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posted by A-Rod 7821 on 11/28/2008 5:03:10 PM  |  status: Live
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El Duderino's comment:
"Thank you"
Response Details:
Use U-Substitution
let u=ln(y)
du=(1/y)dy
ydu=dy
y's cross out you are left with
 OR  ---(ANSWER)---
 
The above guy has the right idea, but didn't realize he needs to substitute back in u=ln(y) after you integrate tan(u)du.
 
 
 
 
 
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posted by Emperor of World on 11/28/2008 7:02:03 PM  |  status: Live
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Response Details:

Use u substitution

u = lny, du = , y du= dy
you can cancel the y, and you will be left just
you know
so
because u=ln y so
 
 
 

 
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posted by LonestarSG on 11/29/2008 11:25:22 AM  |  status: Live
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Response Details:
To answer your question for integrating tangent,


this is a common integral of tan which



you need to memorize (I had to back in high school)

there are more common integrals here:

http://tutorial.math.lamar.edu/pdf/Common_Derivatives_Integrals_Reduced.pdf
Sincerely,
LonestarSG

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