\( F ( x ) = \int _ { 0 } ^ { 1 } \frac { x } { 1 + t ^ { 2 } + \sin ^ { 2 } t } d t \)

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

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

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

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 \( x = 3 \).