\( \int \frac { x ^ { 2 } - 2 x \sin 3 x ^ { 2 } } { x ^ { 3 } + \cos 3 x ^ { 2 } } d x \)

One measure of living standards in country \( A \) is given by the following formula \( L(t)=7+4 e^{0.14 t} \) In this formula \( t \) is the number of years since 1982. Find \( L \) to the nearest hund \( \begin{array}{ll}\text { (a) } 1988 & \text { (b)1998 } \\ \text { (c)2007 }\end{array} \) \( \begin{array}{l}\text { (a) Find } L \text { for } 1988 . \\ \text { (Round to the nearest hundredth as needed.) } \\ \text { (b) Find } L \text { for } 1998 . \\ L=\square\end{array} \) (Round to the nearest hundredth as needed.) (c) Find \( L \) for 2007 .

Analizar en cada caso si es posible aplicar el Teorema de Stokes para calcular la circulación de \( \vec{F} \) a lo largo de \( C:\left\{\begin{array}{l}x^{2}+y^{2}=1 \\ z=0\end{array}\right. \) Hallar el valor de esa circulación. (i) \( \vec{F}=\left\langle\frac{-x}{\left(x^{2}+y^{2}+z^{2}\right)^{3 / 2}}, \frac{-y}{\left(x^{2}+y^{2}+z^{2}\right)^{3 / 2}}, \frac{-z}{\left(x^{2}+y^{2}+z^{2}\right)^{3 / 2}}\right\rangle \)

Encontrar \( f(t) \) si \( \rho(s)=\frac{s}{s^{2}+6 s+10} \)

\( \int \frac { \operatorname { cen } x d x } { \cos x ( \cos x - 1 ) } \)

Ercontrar \( f(t) \) si \( F(s)=\frac{5}{s^{2}+4}+\frac{20 s}{s^{2}+9} \)