Question

$\int (x+5{)}^{2}dx$ . Integrate this using fundamental properties of indefinite integral.

Answer 1

$I=\int (x+5{)}^{2}dx$

$=\int (x^2+10x+25)dx$

$=\int x^{2}dx+(\int 10xdx)+(\int 25dx)$

We know that,

$\int x^{n}dx=\frac{x^{(n+1)}}{n+1}+C$

$I=\frac{x^{2+1}}{2+1}+10\frac{x^{1+1}}{1+1}+25\frac{x^{0+1}}{0+1}+C$

$=\frac{x^3}{3}+10\frac{x^2}{2}+25x+C$