integration question (1 Viewer)

[letsfindlara]

Just wondering if anyone can help me... integrate tanx^5 dx.

I've been trying to figure it out for ages and it's so frustrating!

The first part of the question asked me to find the integrate tanx^3 dx which I found to be (tanx^2)/2 + lncosx + C. I figure there's a connection between tanx^3 and tanx^5. I keep trying to do this: integrate tanx^2 x integrate tanx^3. Is that what I'm supposed to be doing? I can't even work out how to integrate tanx^2!

Thanks in advance for any help.

 

[jyu]

Just wondering if anyone can help me... integrate tanx^5 dx.

I've been trying to figure it out for ages and it's so frustrating!

The first part of the question asked me to find the integrate tanx^3 dx which I found to be (tanx^2)/2 + lncosx + C. I figure there's a connection between tanx^3 and tanx^5. I keep trying to do this: integrate tanx^2 x integrate tanx^3. Is that what I'm supposed to be doing? I can't even work out how to integrate tanx^2!

Thanks in advance for any help.

(tanx)^5 = (tanx)^3 (tanx)^2 =(tanx)^3 ((secx)^2 - 1)
= (tanx)^3 (secx)^2 - (tanx)^3

integ[(tanx)^5]dx = integ[(tanx)^3 (secx)^2]dx - integ[(tanx)^3]dx

etc.

 

[letsfindlara]

Thank you for your help

Haha I feel like a douche bag - right about now

 

[Mark576]

Just curious: would deriving the formula for the area of a circle using integration be considered extension 1 level or extension 2?

 

[Riviet]

Just curious: would deriving the formula for the area of a circle using integration be considered extension 1 level or extension 2?

I'd say extension 1, nothing too out of reach for 3u.