Evaluate the following indefinite integrals:
1. \( \int\left(2 t^{3}-t^{2}+3 t-7\right) d t \)
2. \( \int\left(\frac{4}{z^{7}}-\frac{7}{z^{4}}+z\right) d z \)
3. \( \int\left(3 \sqrt{u}+\frac{1}{\sqrt{u}}\right) d u \)
4. \( \int\left(\sqrt{u^{3}}-\frac{1}{2} u^{-2}+5\right) \)
5. \( \int \frac{2 x^{2}-x+3}{\sqrt{x}} d x \)
6. \( \int \frac{x^{3}+3 x^{2}-9 x-2}{x-2} d x \)
