11. Integrals of Inverse, Exponential, & Logarithmic Functions

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

127. ∫ (ln x) / (x + x ln x) dx

Clever substitution Evaluate ∫ dx/(1 + sin x + cos x) using the substitution x=2 tan⁻¹ θ. The identities sin x = 2 sin(x/2) cos(x/2) and cos x =cos²(x/2) − sin²(x/2) are helpful.