Question

Evaluate the following integrals:

∫ x³ cos x² dx

Answer 1

We can write it as

∫ x.x² cos x² dx

Now let x² = t

2x dx = dt

X dx = dt/2

Now

\(\frac{1}{2}\)∫ t cos tdt

Using BY PART METHOD. Using the superiority list as ILATE (Inverse Logarithm Algebra Trigonometric Exponential). Taking the first function to the one which comes first in the list.

Here t is the first function and cost as the second function.