Example

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

Question

$$\displaystyle\int{ \frac{ 9 { x }^{ 2 } -29x+32 }{ { x }^{ 4 } -6 { x }^{ 3 } +12 { x }^{ 2 } -8x } }d x$$

Answer

$$(d*x*(3*x^2-(29*x)/2+32))/(x-2)^3$$

Solution


Factor out the common term \(x\).
\[\int 9{x}^{2}-29x+32 \, \frac{dx}{x({x}^{3}-6{x}^{2}+12x-8)}dx\]
Rewrite \({x}^{3}-6{x}^{2}+12x-8\) in the form \({a}^{3}-3{a}^{2}b+3a{b}^{2}-{b}^{3}\), where \(a=x\) and \(b=2\).
\[\int 9{x}^{2}-29x+32 \, \frac{dx}{x({x}^{3}-3{x}^{2}(2)+3(x)\times {2}^{2}-{2}^{3})}dx\]
Use Cube of Difference: \({(a-b)}^{3}={a}^{3}-3{a}^{2}b+3a{b}^{2}-{b}^{3}\).
\[\int 9{x}^{2}-29x+32 \, \frac{dx}{x{(x-2)}^{3}}dx\]
Use Power Rule: \(\int {x}^{n} \, dx=\frac{{x}^{n+1}}{n+1}+C\).
\[\frac{dx(3{x}^{2}-\frac{29x}{2}+32)}{{(x-2)}^{3}}\]
[email protected]
Privacy Policy | Terms & Conditions
Contact Us