 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-1/3/i/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

u = x^{2} + 1

d u = 2 x d x

. Then

\int \frac{x}{x ^{2} + 1} d x = x^{2} + 1 + C .

Differentiating verifies this antiderivative on the whole real line.

 New to topics? Read the docs here!