The value of  is

Concept:

Integration by parts: Integration by parts is a method to find integrals of products

• The formula for integrating by parts is given by,
• ∫u v dx = u∫v dx −∫u' (∫v dx) dx

Where u is the function u(x) and v is the function v(x)

ILATE Rule: Usually, the preference order of this rule is based on some functions such as Inverse, Logarithm, Algebraic, Trigonometric and Exponent.

Calculation:

Let I = 

Apply by parts rule, we get

= π3 - 6π

Hence, option (1) is correct.