Question: Determine the following integrals.

1. \[\int \frac{6 x^{2}-6 x}{\left(1-3 x^{2}+2 x^{3}\right)^{\frac{3}{4}}} d x\]
2. \[\int\left[\frac{x}{3 x^{2}+5}-\frac{x^{2}}{\left(x^{3}+1\right)^{3}}\right] d x\]
3. \[\int\left(\frac{2}{t^{2}} \sqrt{\frac{1}{t}+9}\right) d t\]
4. \[\int \frac{2 x}{\left(x^{2}+1\right) \ln \left(x^{2}+1\right)} d x\]
5. \[\int_{-1}^{1}\left(e^{x}-e^{-x}\right)^{2} d x\]
6. \[\int_{3}^{4} \frac{2 x^{4}-6 x^{3}+x-2}{x-2} d x\]
7. \[\int_{\sqrt{2}}^{\sqrt{7}} 3\left(x^{2}+2\right)^{-\frac{1}{2}} x e^{\sqrt{x^{2}+2}} d x\]
8. \[\int_{-2}^{1} 8|x| d x\]

where R, j and \(k\) are constants.

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