I see a handwritten list of indefinite integrals in the image you uploaded. Let me transcribe and solve these one by one. Here’s the list of integrals:

1. $\int \frac{x^2 + 1}{x^2} \, dx$
2. $\int \frac{\sqrt{x}}{1 + 2\sqrt{x}} \, dx$
3. $\int \frac{t}{t^2 + 1} \, dt$
4. $\int \frac{x^2 + 1}{x^3 + 3x + 4} \, dx$
5. $\int \frac{3}{\sqrt{2x + 1}} \, dx$
6. $\int \frac{\ln(2x^2)}{x} \, dx$
7. $\int \frac{6x^2 + 2}{x^3 + x} \, dx$
8. $\int \frac{x}{(3x - 1)^2} \, dx$
9. $\int x\sqrt{2x - 1} \, dx$
10. $\int (1 - \cos t \cot t) \, dt$
11. $\int \sin(2x) \, dx$
12. $\int \cos(6x) \, dx$
13. $\int (\sec u \tan u - \sec^2 u) \, du$
14. $\int \tan^4(x) \sec^2(x) \, dx$
15. $\int \ln(5x) \, dx$

Would you like me to solve all these integrals sequentially, or are there specific ones you'd like to prioritize? Let me know, and I will provide detailed step-by-step solutions!