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Step-by-step Solution
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Divide $x^2+3x$ by $4x^2+9$
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$\begin{array}{l}\phantom{\phantom{;}4x^{2}+9;}{\phantom{;}\frac{1}{4}\phantom{;}\phantom{;}}\\\phantom{;}4x^{2}+9\overline{\smash{)}\phantom{;}x^{2}+3x\phantom{;}\phantom{-;x^n}}\\\phantom{\phantom{;}4x^{2}+9;}\underline{-x^{2}\phantom{-;x^n}-\frac{9}{4}\phantom{;}\phantom{;}}\\\phantom{-x^{2}-\frac{9}{4}\phantom{;}\phantom{;};}\phantom{;}3x\phantom{;}-\frac{9}{4}\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve problems step by step online. Find the integral int((x^2+3x)/(4x^2+9))dx. Divide x^2+3x by 4x^2+9. Resulting polynomial. Expand the integral \int\left(\frac{1}{4}+\frac{3x-\frac{9}{4}}{4x^2+9}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{4}dx results in: \frac{1}{4}x.