Can anyone help to integrat this function please?

eketsaod7

eketsaod7

Answered question

2022-03-18

Can anyone help to integrat this function please?
ic11(2x11+(tcx)2)dt
C>0, x>0 and i the imaginary part
Not really sure how to go about integrating it.

Answer & Explanation

Brock Floyd

Brock Floyd

Beginner2022-03-19Added 6 answers

If x is independent of t, and we have no reason to suppose it isn't, then we can factor it out of the integral and make the substitution u=tcx , as suggested by Gregor Bruns, to get:
ic112x11+(tcx)2=2icxcxcx11+u2xcdu=2icxcx11+u2du
Now you should recognise the integrand as ddutan1(u), so we have
2i[tan1(cx)tan1(cx)]=4itan1(cx)

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