Question

Evaluate $\int x^2\sqrt{x+2}dx$

Answer 1

Solution-

$\int x^2\sqrt{x+2}dx$

put $x+2=tdx=dt$

$\int (t-2{)}^2\sqrt{t}dt$

$\int (t^{5/2}-4t^{3/2}+4\sqrt{t})dt$

$\frac{2}{7}{t}^{7/2}-\frac{8}{5}{t}^{5/2}+\frac{8}{3}{t}^{3/2}+c$

$=\frac{7}{2}(x+2{)}^{7/2}-\frac{8}{5}(x+2{)}^{5/2}+\frac{8}{3}(x+2{)}^{5/2}+c$