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You've uploaded an image with a list of integrals for selection and solving. Let's break down and solve six integrals that you might find interesting from the image. If you have any preferences, feel free to specify them. Otherwise, I'll proceed with choosing six integrals randomly and solve them step by step.

I'll pick the following integrals for now:

1. \(\int (x + 7) \, dx\) [#15]
2. \(\int (x^3 - 1) \, dx\) [#18]
3. \(\int (x^2 + 2x + 1) \, dx\) [#22]
4. \(\int (3x - 1) \, dx\) [#21]
5. \(\int 3x e^x \, dx\) [#26]
6. \(\int x^4 \, dx\) [#31]

Let's solve them now!

Select 6 integrals from the list and solve them step by step.

Step-by-step solutions to 6 integrals, covering polynomial and exponential functions. This detailed explanation covers fundamental calculus concepts such as integration formulas for powers of x and the exponential function. Suitable for advanced high school or undergraduate students.

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