For any , evaluate the integral _ 0 ^ 1 (x + x^2 + 1 )^n…

MATHEMATICS · Subjective · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

For any

n > 1

, evaluate the integral

\int_{0}^{\infty} \frac{1}{(x + \sqrt{x^2 + 1})^n} dx.