這題積分怎麼算 不懂(u/(u^1/2)的積分?

此題需利用積分公式 ∫ x^a dx = [ 1/(a+1) ] * x^(a+1) , 其中 a ≠ -1

∫ ( u/√u - 1/√u ) du , from u = 1 to u = 4
= ∫ [ √u - u^(-1/2) ] du
= [ (2/3)*u^(3/2) - 2√u ] , from u = 1 to u = 4
= [ (2/3)*4^(3/2) - 2√4 ] - [ 2/3 - 2 ]
= 16/3 - 4 - 2/3 + 2
= 8/3