Cálculos de Integrais e Resíduos em Análise Complexa

a recπ2 i 1cosπ2 i 2ei ei 2ee2 1cosπ2 i sinπ2 2ee2 1i eαbii eαbii e2αbii 1 ei i cosz 4 eαbii eαbii 4 a sinz i eabii eabi2i i eabi ea 2 ebeai ebeai 2 ebcosa ebcosa 2 eb ebsina 0 isinz cosz ezi ezi ezi ezi coshzi coshxyii coshxcosy0 sinhycoshx1 sinhz1 sinhxyi1 sinhxcosy1 sinhycoshx0 sinhy0 ykπ kℤ sinhzcoshz sinhxcosyexcoshy sinhycoshxex sinhy 2π2πx dx cos2πx 1 2π 1 2π 1 2π 1 π 1 8 x2 dx a ax 2 0 1 2 4µ2 dµ 4 2 lnµ 9 ln9 2 ex dx ex ln3 ln2 1 3 1 2 1 6 4xdx2ydy 122τ7τ21 ττ2112τdτ int01 intx21 uy dy dx fracu2 int01 x x4 dx fracu2 2leftfracx22 fracx55right01 1 frac35 frac275 01 F dr 11y2332x3dxdy289 int11 int11 x2 y3 xy2 dy dx int11 3x 1 y2 dy dx int11 lefty2 3x2 y2right dy dx frac133x2 4 left1 1right dx frac13left3x2 1 1 1right dx 0 0 C ez zizi dz 2πi Reszifzi Reszifzi 2πi ei 2i ei 2i 2πi sin1 1z²1i dz 1z1iz1i dz 2πi 1221 1201 0 z²u dz 0 1z³ dz 2πi Ref 0 2πi0 0 z 1 zz iz 3i dz 2πi Resf 0 Resf i Resf 3i 2πi 0 0 1 z3 2iz2 dz 1 z2z 2i dz 2πi Resf 0 Resf 2i I1 2pi i cdot z0 cdot f1 f4 2pi i leftfracu 2i5right intC fracz4z2 5z 4 dz 0 intC extcothz dz 2pi i