Learn how to solve problems step by step online. Find the integral int((x^2)/((49+x^2)^2))dx. Rewrite the fraction \frac{x^2}{\left(49+x^2\right)^2} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{49+x^2}+\frac{-49}{\left(49+x^2\right)^{2}}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{49+x^2}dx results in: \frac{1}{7}\arctan\left(\frac{x}{7}\right). The integral \int\frac{-49}{\left(49+x^2\right)^{2}}dx results in: -\frac{1}{7}\left(\frac{1}{2}\arctan\left(\frac{x}{7}\right)+\frac{7x}{2\left(49+x^2\right)}\right).

Find the integral int((x^2)/((49+x^2)^2))dx