Exercise
$\int_1^{\infty}\left(\frac{x\ln\left(x\right)}{\left(1+x^2\right)^2}\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate the function (xln(x))/((1+x^2)^2) from 1 to infinity. Expand the expression \left(1+x^2\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. We can factor the fourth degree trinomial 1+2x^2+x^{4} by applying the substitution: y=x^2. The trinomial y^2+2y+1 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula.
Integrate the function (xln(x))/((1+x^2)^2) from 1 to infinity
Final answer to the exercise
The integral diverges.