​$$\text { Evaluate } \int x\left(x^2-7\right)^{15} d x \text {. }$$​​

Correct option is C

​$$\begin{aligned}&\text{Let:} \\&\quad u = x^2 - 7 \\[10pt]&\text{Then, the derivative of } u \text{ with respect to } x \text{ is:} \\&\quad \frac{du}{dx} = 2x \Rightarrow du = 2x \, dx \Rightarrow x \, dx = \frac{du}{2} \\[10pt]&\textbf{Step 2: Rewrite the Integral in Terms of } u \\&\text{Substitute } u \text{ and } x \, dx \text{ into the integral:} \\&\quad \int x(x^2 - 7)^{15} dx = \int u^{15} \cdot \frac{du}{2} = \frac{1}{2} \int u^{15} \, du \\[10pt]&\textbf{Step 3: Integrate with Respect to } u \\&\text{Integrate } u^{15}: \\&\quad \frac{1}{2} \int u^{15} \, du = \frac{1}{2} \cdot \frac{u^{16}}{16} + C = \frac{u^{16}}{32} + C \\[10pt]&\textbf{Step 4: Substitute Back for } x \\&\text{Replace } u \text{ with } x^2 - 7: \\&\quad \frac{u^{16}}{32} + C = \frac{(x^2 - 7)^{16}}{32} + C\end{aligned}$$​​