Tolong jawab plissshari ini mau dikumpull

Tolong jawab plissshari ini mau dikumpull

$int limits_{0}^{1} {( {x}^{2} + 1) }^{4} x : dx$

misal

$u = {x}^{2} + 1 \ du = 2x : dx \ frac{du}{2} = x : dx$

ubah batas substitusi ke u

$0 to : {0}^{2} + 1 = 1 \ 1 to : {1}^{2} + 1 = 2$

maka integralnya

$int limits_{0}^{1} {( {x}^{2} + 1) }^{4} x : dx \ = int limits_{1}^{2} {u}^{4} : frac{du}{2} \ = frac{1}{2} int limits_{1}^{2} {u}^{4} : du \ = frac{1}{2} ( frac{1}{5} {u}^{5} ) |_{1}^{2} \ = frac{1}{10} ( {2}^{5} - {1}^{5} ) \ = frac{1}{10} (32 - 1) \ = frac{31}{10}$