Integration by Parts - Proving Question (1 Viewer)

[cutemouse]

Hello,

I'm having a problem with the following proving question for integration by parts:

Show that ∫cosecx.dx=ln(tan[x/2])

Thanks anyone who can help me.

Cheers

 

[jpmeijer]

I'm having a problem with the following proving question for integration by parts:

Are you sure it asked for integration by parts? Because it rolls out quite easily using the substitution t = tan(x/2)

 

[cutemouse]

Uhh,

I'll try it with t-results.

Thanks

 

[cutemouse]

Hello,

I still can't prove it using t-results. Could someone please do it me?

Thanks

 

[tommykins]

t = tan [x/2]
x/2 = atan t
1dx/2 = 1dt/1+t^2
2dt/1+t^2 = dx

cosec x = 1/sinx = 1+t^2/2t

int cosecx dx = int (1+t^2)/2t*2/(1+t^2) dt
= 1/t
= ln t + c
= ln [tan x/2]