¿Cuál es el resultado del cálculo de la siguiente integral? \[ \int\left(5 x^{3}-2 x^{2}+3 x-4\right) d x \]

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

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

June 2018 ZIMSEC Paper 1 Solve the equations: \( e^{2 x}=4 e^{2-x} \) giving the answer in exact form. November 2010 ZIMSEC Paper 1

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

(c) \( \int_{6}^{0}(2+5 x) e^{\frac{1}{3} x} d x \)