Evaluate the following Integrals:
Let
Note that we can write cos5x = cos4x × cos x
⇒ cos5x = (cos2x)2 × cos x
We also have sin2x + cos2x = 1
⇒ cos5x = (1 – sin2x)2cos x
So,
Put sin x = t
⇒ cos x dx = dt (Differentiating both sides)
When x = 0, t = sin 0 = 0
So, the new limits are 0 and 1.
Substituting this in the original integral,
Recall