how do i integrate this

[gritty radish]

<@&791435371564892232>

pls help

explain it step by step

[unique sentinel]

,w 8tanx/(1+sin^2(x))

[topaz wave]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by pianotate

[unique sentinel]

hmm

theres an ln involved

[gritty radish]

2ln(2-cos^2x)-4ln(cosx)+c

u=1+sin^2 x?

[unique sentinel]

why 2x

[gritty radish]

oh my bad

[unique sentinel]

have you got it?

ive managed to integrate it cba to put limits in

[tame kite]

i told you how to do it mate

write sin as tan/sec

and then do u sub as u = tan x

so the sec's cancel out

[blissful holly]

How did you do it?

[tame kite]

omg

[reef cloud]

😭

[onyx steeple]

Just not rated

[unique sentinel]

let u = 1 + sin^2x

do all the simplifying stuff

and you'll end up with sec^2x / u, with 4 outside the integral

we need to get sec^2x in terms of u, and you can do this using the pythag trig identity

u - 1 = sin^2x

(u-1) + cos^2x = 1

cos^2x = 1 - u + 1

cos^2x = 2 - u

reciprocate both sides

sec^2x = 1/2-u

so now we have

1/2-u / u --> 1/(2-u)u

do partial fractions

integrate to get ln's and yeah