Evaluate the following integrals:

We will use basic formula : (a + b)² = a² + b² + 2ab

Or, a² + b² = (a + b)² -2ab

Here,

=

Applying above formula, we get,

x⁴ + 1 = (x² + 1)² - 2 × 1 × x²

=

Hence, =

Separate the numerator terms,

=

{ add and subtract 2 to the second term)

=

{ }

=

=

{ since }

=