Question

Evaluate:${\int }_1^3{(x^2+3)}^{2}dx$

Answer 1

${\int }_1^3{(x^2+3)}^{2}dx$

$={\int }_1^3(x^4+6x^2+9)dx$

$={[\frac{x^5}{5}+\frac{6x^3}{3}+9x]}_1^3$

$={[\frac{x^5}{5}+2x^3+9x]}_1^3$

$=[\frac{(3^5-1^5)}{5}+2(3^3-1^3)+9(3-1)]$

$=\frac{242}{5}+52+18$

$=\frac{242}{5}+70$

$=\frac{242+350}{5}=\frac{592}{5}$