\( \int_{0}^{\pi / 6} 9 \sec ^{2} x d x=\square \) (Type an exact answer.)

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

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

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

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

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