Calculate the definite integral of x/(cosh(x))^n from 0 to infinity.

Published on December 5, 2024

Calculus

The integral \int_{0}^{\infty} \frac{x}{(\cosh x)^2} dx evaluates to ln(2).

Question

Integration from zero to infinity of x/(coshx)^n

The eigenvalues of the matrix [[3, 1], [1, 3]] are 4 and 2.

The eigenvalues of the matrix [[0, 1], [-1, 0]] are i and -i.

The eigenvalues of the given 3x3 matrix are 1, 2, and 2.

The determinant of the given 4x4 matrix is calculated using cofactor expansion along the fourth row, resulting in a determinant of -21.

The determinant of the 2x2 matrix [[2, 2], [3, 5]] is calculated as (2 * 5) - (2 * 3) = 4.

The determinant of the 3x3 matrix is calculated using the formula a(ei - fh) - b(di - fg) + c(dh - eg), resulting in a determinant of 0.