Question: 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

(a)

(b) \[\left\{ \frac{1}{2\sqrt{t}}-\frac{3}{{{t}^{{3}/{2}\;}}} \right\}dt\]

(c)

(d) \[\frac{1}{\left( 5{{x}^{2}}-2x-4 \right)}\,\ dx\]

(e)

(f) \[\frac{{{x}^{2}}}{\left( x+1 \right)\,{{\left( x-1 \right)}^{2}}}\,\,dx\]