Example

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

Question

$$\int\frac{2x^{3}+6x^{2}+7x}{(x-2)^{2}(x+1)^{2}}dx$$

Answer

$$(e^2*IM*n*t^2*g*r*a*x^2*d*(2*x^2+6*x+7))/((x-2)^2*(x+1)^2)$$

Solution


Factor out the common term \(x\).
\[\imath ntegrate\times \frac{x(2{x}^{2}+6x+7)}{{(x-2)}^{2}{(x+1)}^{2}}dx\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{\imath ntegratex(2{x}^{2}+6x+7)dx}{{(x-2)}^{2}{(x+1)}^{2}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{\imath n{t}^{2}{e}^{2}gra{x}^{2}(2{x}^{2}+6x+7)d}{{(x-2)}^{2}{(x+1)}^{2}}\]
Regroup terms.
\[\frac{{e}^{2}\imath n{t}^{2}gra{x}^{2}d(2{x}^{2}+6x+7)}{{(x-2)}^{2}{(x+1)}^{2}}\]
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