Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\displaystyle\int{ \frac{ x }{ { x }^{ 2 } -3x+2 } }d x$$

Answer

$$(x^3*d)/(2*(x-2)*(x-1))$$

Solution


Factor \({x}^{2}-3x+2\).
\[\int x \, \frac{dx}{(x-2)(x-1)}dx\]
Use Power Rule: \(\int {x}^{n} \, dx=\frac{{x}^{n+1}}{n+1}+C\).
\[\frac{{x}^{3}d}{2(x-2)(x-1)}\]
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