Use integration by parts to evaluate the integral \( \int x e^{x} \, dx \).

\( \int _ { 0 } ^ { 45 } \sec ^ { 4 } x d x = \)

1) Dada la expresión para la función \( F(x) \) : \[ F(x)=\int_{-2 x}^{2 x^{2}-2 n(x)} \sin (t) d t \] encontrar \( F^{\prime}(x) \). Calcule los valores de las funciones trigonométricus usando los ángulos en radanes.

valuar las siguientes i \( \int \sqrt{3-2 x} x^{2} d x \)

Sociologists have found that crime rates are influenced by temperature. In a town of 100,000 people, the crime rate has been approximated as \( \mathrm{C}=\frac{1}{10}(\mathrm{~T}-60)^{2}+100 \), where C is the humber of crimes per month and \( T \) is the average monthly temperature in degrees Fahrenheit. The average temperature for May was \( 72^{\circ} \) and by the end of May the temperature was rising at the rate of \( 7^{\circ} \) per month. How fast is the crime rate rising at the end of May? At the end of May, the crime rate is rising by (Simplify your answer.)

\( \int _ { 0 } ^ { 45 } \sec ^ { 4 } x d x \)