Integration by substitution help

[fstam2]

I am going crazy on this problem:

\int sec(v+(\pi/2)) tan(v+\pi/2)) dv

if I substitute u= tan(v+\pi/2)) dv, can I use the product rule to find du= sec(v+(\pi/2)) dv.

Thanks, Todd

 

[Galileo]

Use \sin(x+\pi/2)=\cos(x) and \cos(x+\pi/2)=-\sin(x) to rewrite the integrand. Then subsitute u=\frac{1}{\sin(x)}.

 

[dextercioby]

Else,use the definition and the substitution x+\frac{\pi}{2}=u...It's really simple.

And another one:
d[\sec(x+\frac{\pi}{2})]=\sec(x+\frac{\pi}{2})\tan(x+\frac{\pi}{2})dx

so the integration is immediate...

Daniel.