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Natkirky

Member

Registered: 2006-10-17

Posts: 21

Change of Variable

Hi, I am just finishing my first year at Uni.

I was wondering if someone could help me with this question?

∫Tan^4x dx.

I Have a solution for this however, I don't really understand where the values are coming from and I also done a search online and got completely different answers.

We were given this before we done partial fractions and integration by parts so i'm pretty sure the solution should not have anything like that in it.

The solution I have from Uni is 1/6 tan^6x + 1/4 tan^4x + c.  By taking u=tanx.  Now the answers i have been finding online are 1/3 tan^3x - tanx + x + c, this solution makes sense to me and its close to what i got first time I am just worried it's very different from the solution I have from Uni.

I would be very grateful for any help.

Thank you

Bob

Administrator

Registered: 2010-06-20

Posts: 10,624

Re: Change of Variable

hi Natkirky

Try substituting u = tan² x and make use of du/dx = sec² x and also 1 + tan² x = sec² x.

LATER EDIT.  THIS DOESN'T WORK. 

Bob

Last edited by Bob (2011-04-15 00:53:31)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Natkirky

Member

Registered: 2006-10-17

Posts: 21

Re: Change of Variable

Hi Bob,

Thanks for your help can I double check you mean u = tan²x and not tanx as I was sure the derivative of tanx was sec²x.

By using the trig identities I managed to get   du = sec²x dx which is du = (1 + u²) dx.  It was at this point I started to struggle i was not sure where to go from here.

Thanks again for your help

Bob

Administrator

Registered: 2010-06-20

Posts: 10,624

Re: Change of Variable

hi Natkirky,

This version was wrong so I've deleted the evidence!  Sorry about that.

The one below is my new version

Bob

Last edited by Bob (2011-04-15 00:48:37)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Natkirky

Member

Registered: 2006-10-17

Posts: 21

Re: Change of Variable

Hi Bob,

That's great I keep getting mixed up with the sec and tan ones.  I see what you are doing it's a big help thanks very much. 

Bob

Administrator

Registered: 2010-06-20

Posts: 10,624

Re: Change of Variable

hi Natkirky,

What I posted above is wrong.  So sorry.  I've got my du/dx upside down so here is my re-think

These terms are all directly integrable :

That's the on-line answer you had above.

Bob

Last edited by Bob (2011-04-15 00:51:59)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob