Encontrar \( f(t) \) si \( \rho(s)=\frac{s}{s^{2}+6 s+10} \)

Calcule a integral definida \( \int_{0}^{3} (2x^2 + 4) \, dx \).

Residues at Poles - Example 1 The function \( \quad f(z)=\frac{z+1}{z^{2}+9} \) has an isolated singular point at \( \mathrm{z}=3 \mathrm{i} \) and can be written

Residues at Poles = Proof the Theorem Assume \( f(z) \) has the following form \[ f(z)=\frac{\phi(z)}{\left(z-z_{0}\right)^{m}} \] where \( \varphi(\mathrm{z}) \) is analytic and nonzero at \( \mathrm{z}_{0} \), then it has Taylor series representation

Find the derivative of \( f(w)=\frac{3}{\left(w^{2}-6\right)^{5}} \)

Calculate the area under the curve defined by the function \( f(x) = x^3 + 2x - 1 \) from \( x = 1 \) to \( x = 3 \).