How do you use substitution to integrate sec(v + pi/2) * tan(v + pi/2)?

1 Answer
Sep 22, 2015

See the explanation.

Explanation:

t=1/sec(v+pi/2)

dt=((sec(v+pi/2))^-1)'dv=

dt=-1/sec^2(v+pi/2)sec(v+pi/2)tan(v+pi/2)dv

dt=-(tan(v+pi/2)dv)/sec(v+pi/2)=-t tan(v+pi/2)dv

tan(v+pi/2)dv=-dt/t

int sec(v+pi/2) tan(v+pi/2) dv=int 1/t(-dt/t)=

=-int t^-2dt=1/t+C=sec(v+pi/2)+C