Integrate the function $\frac{x^2\cos\left(\frac{x}{5}\right)}{\left(x^2+25\right)^2}$ from 0 to $\infty $

Learn how to solve problems step by step online. Integrate the function (x^2cos(x/5))/((x^2+25)^2) from 0 to infinity. Expand the expression \left(x^2+25\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. We can factor the fourth degree trinomial x^{4}+50x^2+625 by applying the substitution: y=x^2. The trinomial y^2+50y+625 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula.