Find the integral of $\frac{-2x}{\left(x^2+2x+2\right)^2}$

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$\int\frac{-2x}{\left(x^2+2x+2\right)^2}dx$

Learn how to solve inequalities problems step by step online. Find the integral of (-2x)/((x^2+2x+2)^2). Find the integral. Take out the constant -2 from the integral. Rewrite the expression \frac{x}{\left(x^2+2x+2\right)^{2}} inside the integral in factored form. We can solve the integral \int\frac{x}{\left(1+\left(x+1\right)^2\right)^{2}}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x+1 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.