### Home > CALC > Chapter 10 > Lesson 10.2.2 > Problem10-108

10-108.

You should recognize the integrand as a form of the derivative of tan–1(x).
The denomintor needs to be of the form a2 + 1.

$\frac{1}{x^2+4}=\frac{1}{4(x^2/4+1)}=\frac{1}{4((x/2)^2+1)}$

Use substitution. Let u = x2 + 4.

Factor the denominator then use partial fraction decomposition.

$\frac{x^2}{x^2+4}=\frac{x^2+4-4}{x^2+4}=1-\frac{4}{x^2+4}$