More Ext2 Integration help needed please (1 Viewer)

[blackops23]

Hi, I'm having trouble with a few questions:

Q1. integrate: (sec^2 x)/(tan^2 x -1)

so I let u=tanx, and ended up having to integrate 1/(u^2 -1). How do I integrate this? The table of standard integrals doesn't specify a particular way to integrate this, so could some please shed some light?

Q2. integrate (cosx)/(1-sin^2 x)

Now I saw two ways to do this, first method involves changing the denominator to cos^2 x, meaning you have to integrate secx. How do you do this?

2nd method, ,you let u=sinx, meaning you have to integrate 1/(1-u^2). How do you do this??

Thank you, help is greatly appreciated.

 

[Aindan]

Q1. Use partial fractions. u^2 - 1 = (u+1)(u-1)
Q2. method a). Integrate sec x by multiplying by 1 (secx + tanx), should become a log.
method b). use partial fractions again

 

[blackops23]

Q1. Use partial fractions. u^2 - 1 = (u+1)(u-1)
Q2. method a). Integrate sec x by multiplying by 1 (secx + tanx), should become a log.
method b). use partial fractions again

Thankyou for the prompt reply. But if you were to do these questions, would you follow the same methods/substitution I used, or do you see a different more approachable way?

 

[funnytomato]

Thankyou for the prompt reply. But if you were to do these questions, would you follow the same methods/substitution I used, or do you see a different more approachable way?

wat?

 

[blackops23]

wat?

Are there alternative methods/substitutions?

 

[funnytomato]

Are there alternative methods/substitutions?

ur way was probably the simplest

 

[muzeikchun852]

 

[blackops23]

matee.... pretty sure tan^2 x +1 = sec^2 x

not tan^2 x -1 = sec^2 x

 

[muzeikchun852]

matee.... pretty sure tan^2 x +1 = sec^2 x

not tan^2 x -1 = sec^2 x

sorry my bad.

 

[blackops23]

Hi, here's another question that I am having a lot of trouble with;

Q. integrate 1/(x^3 -1)

I used the partial fractions method, which led me to integrate the following expression:

1/[3(x-1)] - (x+2)/[3(x^2 + x +1)] dx

Now I know how to integrate 1/3(x-1)...

but HOW do i integrate (x+2)/(3(x^2 + x+1))

Help on this is immensely appreciated

 

[funnytomato]

to integrate x+2 / x^2+x+1 , write x+2 as (2x+1)/2 + 3/2 so you can express x+2 / x^2+x+1 as ( 2x +1 / x^2+x+1)/2 and 1.5/ x^2+x+1
which are log and inverse tan respectively

 

[funnytomato]

also I factorised 1/3 at the very front

 

[K4M1N3]

For the initial question, has anyone realised that the derivative is on the top....

 

[funnytomato]

For the initial question, has anyone realised that the derivative is on the top....

5/(1/4-1)= 5*(4-1)?

 

[funnytomato]

trollololololololol...

 

[stampede]

For the initial question, has anyone realised that the derivative is on the top....

 

[stampede]

integrate (x+2)/(3(x^2 + x+1))

you should be able to do these now