- #1
AStaunton
- 105
- 1
problem is to integrate the following by parts:
[tex]\int x\sec^{2}xdx[/tex]
my feeling is convert the secant term to cosine by:
[tex]sec^{2}x=cos^{-2}x\Rightarrow\int\sec^{2}xdx=\int\cos^{-2}xdx[/tex]
then:
[tex]u=\cos^{-2}x\implies du=2\sin x(\cos^{-3}x)[/tex]
and also:
[tex]dv=xdx\implies v=\frac{x^{2}}{2}[/tex]
however plugging all this into int. by parts equation ends up with:
[tex]\frac{x^{2}}{2}\cos^{-2}x-\int2\frac{x^{2}}{2}\sin x\cos^{-3}xdx[/tex]
which seems to be an even more complicated integral...
is my idea of converting the secant to cosine a good or does it make more complicated?
any advice appreciated
[tex]\int x\sec^{2}xdx[/tex]
my feeling is convert the secant term to cosine by:
[tex]sec^{2}x=cos^{-2}x\Rightarrow\int\sec^{2}xdx=\int\cos^{-2}xdx[/tex]
then:
[tex]u=\cos^{-2}x\implies du=2\sin x(\cos^{-3}x)[/tex]
and also:
[tex]dv=xdx\implies v=\frac{x^{2}}{2}[/tex]
however plugging all this into int. by parts equation ends up with:
[tex]\frac{x^{2}}{2}\cos^{-2}x-\int2\frac{x^{2}}{2}\sin x\cos^{-3}xdx[/tex]
which seems to be an even more complicated integral...
is my idea of converting the secant to cosine a good or does it make more complicated?
any advice appreciated