List of Non-elementary Integrals and Sums in Text

If a > 0 constant,

ln[a sin(x)]dx = 1

ln[a sin(x)]dx = π

2 ln (a 2

) .

(Problems 2.1.16, 3.2.26 (d), 3.7.88. Example 3.7.47.)

13. ∫ π/2 0

ln[tan(x)] dx = 0 and

ln[| tan(x)|] dx = 0.

(Problem 2.1.18.)

14. ∫ ∞ 0

ln(x)

x2 + 1 dx = 0.