Evaluate the integral \( \int (3x^2) \cdot e^{x^3} \, dx \) using substitution.

Determine la longitud de la curva \( x=\frac{y^{5}}{5}+\frac{1}{12 y^{3}} \) en el intervalo \( y \in[1,2] \). resultado con dos decimales.

Find the value. \[ \begin{array}{l}\operatorname{In}\left(\frac{92}{20}\right) \\ \text { In }\left(\frac{92}{20}\right) \approx \square \\ \text { (Round the final answer to four decimal places as needed. Round }\end{array} \]

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

Given the system of differential equations: \[ \frac{d \mathbf{x}}{d t}=A \mathbf{x} \] where \( A=\left(\begin{array}{ll}4 & 0 \\ 0 & 3\end{array}\right) \), what is the general solution for \( \mathbf{x}(t) \) ?

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