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

Instructions:

writing an assigment on integration

source..Content:

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

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