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Mathematics 21 Online
OpenStudy (studygurl14):

Antiderivative of.... @mathmale @ganeshie8 @ParthKohli @pooja195 @freckles @mathstudent55 @tkhunny

OpenStudy (studygurl14):

What do I use for u-substitution? \(\Large \csc(2x)\cot(2x)\)

OpenStudy (studygurl14):

@mathmale @ganeshie8 @ParthKohli @pooja195 @freckles @mathstudent55 @tkhunny

OpenStudy (er.mohd.amir):

use cos 2x/sin2x *sin2x put sin 2x=t

OpenStudy (er.mohd.amir):

since csc x=1/sin x and cot x=cosx /sin x

OpenStudy (studygurl14):

Okay, I see what you're saying. I'll try that

OpenStudy (studygurl14):

Awesome, I think it worked. so far I have 1/u du, which can easily be solved now. Tahnks!

OpenStudy (studygurl14):

wait, no...

OpenStudy (er.mohd.amir):

1/u^2 du

OpenStudy (studygurl14):

the antiderivative of 1/u = ln x

OpenStudy (er.mohd.amir):

there is sin2x is squre

OpenStudy (studygurl14):

oh, right! two sin 2x. forgot the exponent 2

OpenStudy (studygurl14):

is it -csc 2x?

OpenStudy (studygurl14):

@Er.Mohd.AMIR Is that the correct antiderivative?

OpenStudy (er.mohd.amir):

(-1/2 ) cse 2x

OpenStudy (studygurl14):

how'd you get the 1/2 part?

OpenStudy (er.mohd.amir):

sin 2x =u cos 2x .2 .dx=du

OpenStudy (er.mohd.amir):

cos 2x dx=1/2 du

OpenStudy (er.mohd.amir):

got it

OpenStudy (studygurl14):

Oh, I forgot to apply the chainrule when finding du/dx

OpenStudy (studygurl14):

Thank you. :)

OpenStudy (er.mohd.amir):

welcome

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