Calculus, 2ADV, EQ-Bank 17 Find \(\displaystyle \int x\left(x^2+1\right)^3\, d x\). (2 marks) --- 6 WORK AREA LINES (style=lined) --- Show Answers Only \(\dfrac{1}{8}\left(x^2+1\right)^4+c\) Show Worked Solution \(\displaystyle\int x\left(x^2+1\right)^3\, d x\) \(=\dfrac{1}{2} \displaystyle \int 2 x\left(x^2+1\right)^3 d x\) \(=\dfrac{1}{2} \times \dfrac{1}{4}\left(x^2+1\right)^4+c\) \(=\dfrac{1}{8}\left(x^2+1\right)^4+c\)