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Solve the following integral: $$ \int (2x^3 - 3x^2 + x - 5) \, dx $$
Answer: 12x4−x3+12x2−5x+C
Find the solution to the differential equation: $$ \frac{dy}{dx} + 2y = e^{3x} $$
Answer: y=Ce−2x+e3x5
Calculate the limit: $$ \lim_{{x \to 0}} \frac{\sin(5x)}{x} $$
Answer: 5
Determine the eigenvalues of the matrix: $$ \begin{pmatrix} 4 & 1 \\ 2 & 3 \end{pmatrix} $$
Answer: 55 and 2
Evaluate the following sum: $$ \sum_{{n=1}}^{\infty} \frac{1}{n^2} $$
Answer: π26