https://file.aiquickdraw.com/mathbot/file/1726694363576hj2sxvr1.jpg

The image contains a set of mathematical problems. Let's break them down:

### Task 1 (Зад. 1):
Solve the following system of linear equations:
\[
\begin{cases}
3x_1 - x_2 + x_3 = 5 \\
x_1 + 2x_3 = 2 \\
x_1 - 2x_2 - x_3 = 0
\end{cases}
\]

### Task 2 (Зад. 2):
Given points:
- \( A(2, -2) \)
- \( B(-1, 0) \)
- \( C(3, -4) \)

Find some geometrical property (probably a line equation or something related).

### Task 3 (Зад. 3):
The function given is:
\[
y = \frac{3x}{e^{2x + 1}}
\]
Differentiate or analyze the behavior of the function.

### Task 4 (Зад. 4):
The expression is:
\[
z = 2xy - x^2 + 3y^2 - 2x
\]
Likely requiring partial derivatives or critical point analysis.

### Task 5 (Зад. 5):
Three integrals:
1. \( \int \frac{dx}{x(1 + 2 \ln x)} \)
2. \( \int (2 - x) e^{3x} \, dx \)
3. \( \int_1^2 \frac{dx}{(4 - x)^3} \)

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Which of these would you like to tackle first? Would you like details for one specific task?

The image contains five mathematical problems. They include solving a system of equations, finding properties of points, differentiating a function, analyzing an expression, and evaluating integrals.

Solve advanced university-level math problems including systems of linear equations, coordinate geometry, differentiating exponential functions, and evaluating integrals. Step-by-step solutions provided for calculus and algebra topics.

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