Integrate: ∫ 8^x cot^2(8x)dx

Answer 1

Let u = 8^x

Then du = (ln8)8^xdx.

So, 8^xdx = (1/ln8)du

The integral can then be rewritten as (1/ln8)∫cot²udu

= (1/ln8)∫[csc²u - 1]du

= (1/ln8)[-cotu - u) + C

= (1/ln8)[-cot(8^x) - 8^x) + C

Answer 2

No, you must integrate it numerically .

Please specify the limits of integration so we can run it through Simpson's Rule