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Contour integral, Continue of this question https://www.chegg.com/homework-help/questions-and-answers/contour-integral-considering-integral-suitably-chosen-contour-cut-z-plane-prove-q38104428 With fo...

Contour integral, Continue of this question

https://www.chegg.com/homework-help/questions-and-answers/contour-integral-considering-integral-suitably-chosen-contour-cut-z-plane-prove-q38104428

With following data

\int_{0}^{\infty }\frac{log^{2}(t)-\pi^{2}}{t^{\frac{1}{2}}(1+t^{2})}dt=\frac{-\pi^{3}}{4\sqrt{2}}

And using the same integration contour as in part (a) with the integrand log(z) , find a relation between the integrals

30log (t) dt (1+1) 1 t 0 and 2 o ti(1t)

Use this relation to deduce, without further contour integration, that

1 o t(1t) 2


log(z)
30log (t) dt (1+1) 1 t 0
2 o ti(1t)
1 o t(1t) 2
0 0
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445 dt 2..za t ) 2. 242

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