Final Answer
$6x-36\arctan\left(\frac{x}{6}\right)+C_0$
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Step-by-step Solution
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1
Take out the constant $6$ from the integral
$6\int\frac{x^2}{36+x^2}dx$
Learn how to solve integrals of rational functions problems step by step online.
$6\int\frac{x^2}{36+x^2}dx$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((6x^2)/(36+x^2))dx. Take out the constant 6 from the integral. Divide x^2 by 36+x^2. Resulting polynomial. Expand the integral \int\left(1+\frac{-36}{36+x^2}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.
Final Answer
$6x-36\arctan\left(\frac{x}{6}\right)+C_0$