Final answer to the problem
Step-by-step Solution
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Divide $40-6x+x^2$ by $x^2-9x$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x^{2}-9x\phantom{;};}{\phantom{;}1\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-9x\phantom{;}\overline{\smash{)}\phantom{;}x^{2}-6x\phantom{;}+40\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-9x\phantom{;};}\underline{-x^{2}+9x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{2}+9x\phantom{;};}\phantom{;}3x\phantom{;}+40\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((40-6xx^2)/(x^2-9x))dx. Divide 40-6x+x^2 by x^2-9x. Resulting polynomial. Expand the integral \int\left(1+\frac{3x+40}{x^2-9x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int1dx results in: x.