Question

Evaluate the following integrals:

∫ e^x (tan x - log cos x) dx

Answer 1

∫ e^x (tan x - log cos x) dx

Tip – If f₁(x) and f₂(x) are two functions , then an integral of the form ∫ f₁(x)f₂(x)dx can be INTEGRATED BY PARTS as

where f₁(x) and f₂(x) are the first and second functions respectively.

Taking f₁(x) = log cos x and f₂(x) = e^x in the second integral and keeping the first integral intact,

where c is the integrating constant