(1)- \( \int_{-\infty}^{\infty} \frac{e^{x}}{1+e^{2 x}} \mathrm{dx} ? \)

Check whether the differential equation: Is Exact or not? If yes, \( \frac{\text { find }}{\left(6 x^{2}+4 x y+y^{2}\right) d x+\left(2 x^{2}+2 x y-3 y^{2}\right) d y=0} \).

19. (90-8 - 00 ) Ushbu \( f(x)=\frac{3}{4 \sqrt{16}} \) funksiyaniag bosh- lang ich funksiyasini toping. \( \begin{array}{lll}\text { A) } \frac{3}{2} \sqrt{x}+C & \text { B) } 3 \sqrt{x}+C & \text { C) } \frac{4}{3} \sqrt{x}+C \\ \text { D) }-\frac{3}{2} \sqrt{x}+C & \text { E) } 6 \sqrt{x}+C & \end{array} \)

Find \( y \). \( y^{\prime}=\frac{9}{8 \sqrt{x}} \quad \) Condition: \( y(16)=10 \)

\( f ( x ) = \int e ^ { 58379 } d x \)

\( \operatorname { Lim } _ { n \rightarrow \infty } ( - 1 ) ^ { n } e ^ { x } = \)