Evaluate the definite integral

Question

lower bound = 1 upper bound = e

function = 2t⁴ln(t) dt

This question requires you to integrate in parts. I am having a hard time understanding the concept.

Answer 1

∫₁^e2t⁴lntdt = 2t⁵/5·

By parts:u= lnt; du = dt/t; dv = 2t⁴dt; v = 2t⁵/5·lnt₁^e - ∫₁^e2t⁴/5dt = 2/5e⁵- 2/25t⁵₁^e = 8/25e⁵ + 2/25 = 47.57221091