Question

\(\int\left(2x+1\right)\left(x+3\right)^4dx\)

Answer 1

\(u=x+3\Rightarrow x=u-3\Rightarrow du=dx\)

\(\Rightarrow\int\left(2x+1\right)\left(x+3\right)^4dx=\int\left[2\left(u-3\right)+1\right].u^4du\)

\(=\int\left(2u-5\right)u^4du=\int(2u^5-5u^4)du=\dfrac{2}{6}u^6-\dfrac{5}{5}u^5=\dfrac{1}{3}u^6-u^5=\dfrac{1}{3}\left(x+3\right)^6-\left(x+3\right)^5\)