Question 19 LF. of the differential equation \( \frac{d y}{d x}=500 x^{n}-\frac{y}{x} \), is \( \begin{array}{ll}\text { (a) } x & \text { (b) } 3 x \\ \text { (c) } 2 x & \text { (d) }-2 x\end{array} \)

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

3.2. \( \int \ln 3 x d x \)

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

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

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