Question: Integrate functions using the rules, by parts, by substitution and partial fractions

Integrate the following functions using the appropriate method chosen from the list below:

• basic rules
• by parts
• by substitution
• using reduction formulae
• by using partial fractions

1. 
2. \[\left\{ \frac{1}{2\sqrt{t}}-\frac{3}{{{t}^{{3}/{2}\;}}} \right\}dt\]
3. 
4. \[\frac{1}{\left( 5{{x}^{2}}-2x-4 \right)}\,\ dx\]
5. 
6. \[\frac{{{x}^{2}}}{\left( x+1 \right)\,{{\left( x-1 \right)}^{2}}}\,\,dx\]

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