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The trinomial $x^4+8x^2+16$ is a perfect square trinomial, because it's discriminant is equal to zero
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$\Delta=b^2-4ac=8^2-4\left(1\right)\left(16\right) = 0$
Learn how to solve problems step by step online. Integrate the function (x^2)/(x^4+8x^2+16) from 0 to 1. The trinomial x^4+8x^2+16 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial. We can solve the integral \int\frac{x^2}{\left(x^{2}+4\right)^{2}}dx by applying integration method of trigonometric substitution using the substitution.