The image contains several mathematical problems related to calculus and algebra. Here are the questions extracted from the image:

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Unit IV

1. Find the value of $\int \sin^2 x \, dx$

2. Integrate the following function with respect to $x$:

   $\int x \sqrt{2x + 3} \, dx$

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3. Evaluate $\int x^2 e^x \, dx$

4. Integrate the following function with respect to $x$:

   $\int \frac{x^3}{\sqrt{1 - x^2}} \, dx$

5. Find the area bounded by the curves $y = 2x - x^2$ and $y = x$ with the x-axis.

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Would you like me to solve all of these problems or any specific one?