8. \( \int \sqrt[3]{x}(x+1)^{3} d x= \)

3.3. \( \int \frac{x-1}{\left(x^{2}+1\right)(x+1)} d x \)

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

احسب التكامل لـ \( \frac{4x^3 - 7x + 5}{2x + 1} dx \) من خلال تطبيق طريقة القسمة الطويلة.

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 = 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