Guest Session: 1 Question Remaining. Create Account to save progress.
Login
Integralshard
0:00.0

Evaluate the improper integral I=∫0∞dx(1+x2)(1+ex)I = \int_{0}^{\infty} \frac{dx}{(1+x^2)(1+e^x)}I=∫0∞​(1+x2)(1+ex)dx​. Using the property ∫0∞f(x)dx=∫01f(x)dx+∫1∞f(x)dx\int_0^\infty f(x) dx = \int_0^1 f(x) dx + \int_1^\infty f(x) dx∫0∞​f(x)dx=∫01​f(x)dx+∫1∞​f(x)dx is difficult, so use the symmetry of the integrand. Which of the following is the correct value?