Tìm nguyên hàm \(\int x\left(x^{2}+7\right)^{15} \mathrm{~d} x\)

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\text { Đặt } t=x^{2}+7 \Rightarrow \mathrm{d} t=2 x \mathrm{~d} x \Rightarrow x \mathrm{~d} x=\frac{1}{2} \mathrm{~d} t \\
\text { Ta có } \int x\left(x^{2}+7\right)^{15} \mathrm{~d} x=\frac{1}{2} \int t^{15} \mathrm{~d} t=\frac{1}{2} \cdot \frac{t^{16}}{16}+C=\frac{1}{32}\left(x^{2}+7\right)^{16}+C .
\end{array}\)