Question

Can some one show me all the steps to evaluate the Integral of (tan^3xsec^3x) dx

Answer 1

\[\int\limits(\tan^3xsex^3x)dx \] Thats the problem I have to integrate...

Answer 2

did you try u=sec x ?

Answer 3

\(\int \tan x\sec x\sec^2x(\sec^2x-1)dx\)

Answer 4

then put u=sec x
du ....?

Answer 5

du= sec x tan x?

Answer 6

almost!
du =sec x tan x dx

Answer 7

Haha lol yeah I always forget the dx :P

Answer 8

\(\int u^2(u^2-1)du\)
pretty easier to integrate this.

Answer 9

Okay and you replaced tan^2 with (sec^2x-1)?

Answer 10

yes...

Answer 11

doubts ? any kind ?

Answer 12

So its U^3/3(U^3/3-1)du?

Answer 13

Then I just put back u, which is sec x

Answer 14

what! no... :(
\(\int u^4-u^2 dx\)

Answer 15

*du

Answer 16

Ohh oops XD I didnt know if you were supposed to do the algebra there or not :P

Answer 17

now integrate

Answer 18

Okay so now its u^5/5-u^3/3?

Answer 19

Then replace u with sec x?

Answer 20

now, yes!

Answer 21

So sec^5/5 - Sec^3/3

Answer 22

+c
and correct.

Answer 23

Thanks! :D

Answer 24

welcome ^_^