Example

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

Question

$$\displaystyle\int{ \frac{ 1+ { x }^{ 2 } }{ (x-2) { \left(x+1 \right) }^{ 3 } } }d x$$

Answer

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

Solution


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