Integration Mathematics & Economics Math Problem Paper (Math Problem Sample)

Integration
We are required to determine the indefinite integral
3sec2x-1tan2x-1dx=3sec2x-1tan2x-1dx. (1)
The constant 3 can be taken out of integral as shown in equation (1). Applying u- substitution as shown by (Carl,2003) we let u=2x-1 and so
dudx=2 which implies that dx=du2.
The indefinite integral (1) now becomes
3secutanudu2=32secutanudu.(2)
Applying u-substituion again, we let v=secu and so
dudv=secutanudu, which implies that du=dvsecutanu.
By appropriate substitution, the indefinite integral (2) becomes
32secutanudu=32secutanudvsecutanu=32dv=32v+C. (3)
Here C is an arbitrary constant of integration. Noting that v=secu and u=2x-1, so that we w