Exercise
$\int\frac{\left(x^2+2x+1\right)}{\left(x^2+1\right)^2}dx$
Step-by-step Solution
Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((x^2+2x+1)/((x^2+1)^2))dx. Rewrite the expression \frac{x^2+2x+1}{\left(x^2+1\right)^2} inside the integral in factored form. Rewrite the fraction \frac{\left(x+1\right)^{2}}{\left(x^2+1\right)^2} in 2 simpler fractions using partial fraction decomposition. Simplify the expression. The integral \int\frac{1}{x^2+1}dx results in: \arctan\left(x\right).
Find the integral int((x^2+2x+1)/((x^2+1)^2))dx
Final answer to the exercise
$\arctan\left(x\right)+\frac{1}{-x^2-1}+C_0$