Integration by parts sum class XII

Subject: Integration by parts sum class XII Mon Feb 14, 2011 2:43 pm

Kindly check the working and tell the reason for the wrong answer at the end.Please tell what is wrong with process. I know how to do by other process just want to know why dis is wrong.

I=∫sec3 xdx

=∫secx.sec2xdx

Using By parts formula with secx as u and sec2x as v-

I=secx∫sec2xdx -∫{d/dx(secx) ∫sec2xdx}dx

I=secx.tanx- ∫secxtanx.tanxdx

In ∫tanx.(secxtanx)dx,

Taking tanx as u and secxtanx as v for byparts-

tanx∫secxtanxdx-∫{d/dx(tanx) ∫secxtanxdx}dx

=tanx.secx-∫sec2x.secxdx

Therefore, I=secxtanx-secxtanx+ ∫ sec3 xdx
I=I??

NOTE:sec2x is sec square x and sec3x is sec cubed x

Subject: Re: Integration by parts sum class XII Thu Feb 17, 2011 12:37 pm

I=∫sec3 xdx

=∫secx.sec2xdx

Using By parts formula with secx as u and sec2x as v-

I=secx∫sec2xdx -∫{d/dx(secx) ∫sec2xdx}dx
I=secx.tanx- ∫secxtanx.tanxdx
I = secx.tanx - ∫secx( tan2x)dx,
I = secx.tanx -∫secx( sec2x -1)dx,
I = secx.tanx -∫(sec3x- secx )dx,
I = secx.tanx -∫sec3x+ ∫secx dx,
I = secx.tanx -I+ ∫secx dx,
2I = secxtanx - log( secx + tanx)
I = [secxtanx - log( secx + tanx)]/2