### Need help from an expert?

The world’s top online tutoring provider trusted by students, parents, and schools globally.

The integral of 1/(x^2+1)^2 is (1/2)arctan(x/(x^2+1)) + C.

To solve this integral, we can use the substitution u = x^2 + 1. Then du/dx = 2x, so dx = du/(2x). Substituting these into the integral, we get:

∫ 1/(x^2+1)^2 dx = ∫ 1/u^2 * (du/(2x)) = (1/2) ∫ u^(-2) du

Integrating u^(-2), we get -u^(-1) + C. Substituting back in for u, we get:

(1/2) ∫ (x^2+1)^(-2) dx = (1/2) (-1/(x^2+1)) + C

Simplifying, we get:

(1/2)arctan(x/(x^2+1)) + C

Therefore, the integral of 1/(x^2+1)^2 is (1/2)arctan(x/(x^2+1)) + C.

Study and Practice for Free

Trusted by 100,000+ Students Worldwide

Achieve Top Grades in your Exams with our Free Resources.

Practice Questions, Study Notes, and Past Exam Papers for all Subjects!

The world’s top online tutoring provider trusted by students, parents, and schools globally.

Loading...

Loading...