Example 1: Integrate: ∫sin^{1/3}x cosx dx
Solution:
We could either choose u = sin x, u = sin^{1/3}x or u = cos x. However, only the first one of these works in this problem.
So we let u = sin x.
Finding the differential:
du = cos x dx
Substituting these into the integral gives:
Example 2: Evaluate
Solution:
Example 3: Evaluate ∫15678dx
Solution:
∫15678dx = 15678x+C
Example 4: Evaluate ∫6x^{2} + 4dx
Solution:
∫6x^{2} + 4dx
= 6∫x^{2}dx + 4∫dx
=6x^{3}/3 + 4x + C
= 2x^{3} + 4x + C