Question

Solve: ${\int }_0^1(1+x{)}^{5}dx$

Answer 1

${\int }_0^1{(1+x)}^{5}dx$

Let $1+x=t\Rightarrow dx=dt$

Therefore,

${\int }_1^2{t}^{5}dt$

$={\left[\frac{t^6}{6}\right]}_1^2$

$=\frac{2^6}{6}-\frac{1^6}{6}$

$=\frac{64-1}{6}=\frac{21}{2}$