Question

integral u substitution question

Answer 1

integral (cot2x-csc2x)^2dx

Answer 2

any ideas?

Answer 3

i wud try and simplify the trig part first...

Answer 4

yeah with that I got

Answer 5

cot = cos/sin

csc = 1/sin

Answer 6

yeah cos2x-1/sin2x

Answer 7

and I could use u as sin2x and have du=2cos2xdx but that makes me question what do I do with the 1?

Answer 8

dont do the substitution yet,
it simplifies more..

Answer 9

cos2x-1/sin2x

-2sin^2x / 2sinxcosx

-tanx

Answer 10

dont forget that this thing is under a square

Answer 11

u need to take :

integral (-tanx)^2 dx

Answer 12

thank you so much I did not think of that and i had my identity sheet in front of me

Answer 13

np :)

Answer 14

but what happened to the 2x on the inside when you went to tanx?

Answer 15

see if u can finish it off..

Answer 16

which 2x ?

Answer 17

you have -2sin2x/2sinxcosx and i know that sin over cos is the tanx but how does that go to tanx?

Answer 18

oh my bad sorry misread it

Answer 19

nvm

Answer 20

:) its -2sin^2x in the numerator

Answer 21

so now im stuck again so we end with -tanx which is -sinx/cosx and make u=cosx we have du=-sinxdx so then we have the integral of u^-1 which so far from what I have learned we cant do

Answer 22

whats derivative of 'ln x' ?

Answer 23

yeah we havent done integration with logs yet he told us to skip another one cuz of that

Answer 24

but so derivative of lnx would be 1/x right?

Answer 25

good :) there is a better way

Answer 26

so would the answer be the lnu+c?

Answer 27

use this : tan^2x + 1 = sec^2x

Answer 28

integral tan^2x dx

integral (sec^2x - 1) dx

Answer 29

you must be knowing integrals for sec^2x and 1 ?

Answer 30

yes so it would be -(tanx-x+c)?

Answer 31

or no the negative goes away because of the ^2?

Answer 32

from where "-" is coming ha ?
it should be just :

tanx -x + c

Answer 33

^^yess..

Answer 34

thank you for all your help

Answer 35

np :)