We have given

\(\int x^2 6^{x^3+8}dx\)

\(\text{Take }x^2 6^{x^3+8}\)

\(\Rightarrow 3x^2dx=dt\)

\(\Rightarrow x^2dx=\frac{dt}{3}\)

\(\text{Then,}\)

\(\int x^2 6^{x^3+8}=\frac{1}{3}\int6^tdt\)

\(=\frac{1}{3}\frac{6^t}{\ln(6)}\)

\(=\frac{1}{3}\cdot\frac{6^{x^3+8}}{\ln(6)}\)

\(=\frac{6^{x^3+8}}{3\ln(6)}\)

\(\text{Therefore,}\)

\(\int x^2 6^{x^3+8}dx=\frac{6^{x^3+8}}{3\ln(6)}\)

\(\int x^2 6^{x^3+8}dx\)

\(\text{Take }x^2 6^{x^3+8}\)

\(\Rightarrow 3x^2dx=dt\)

\(\Rightarrow x^2dx=\frac{dt}{3}\)

\(\text{Then,}\)

\(\int x^2 6^{x^3+8}=\frac{1}{3}\int6^tdt\)

\(=\frac{1}{3}\frac{6^t}{\ln(6)}\)

\(=\frac{1}{3}\cdot\frac{6^{x^3+8}}{\ln(6)}\)

\(=\frac{6^{x^3+8}}{3\ln(6)}\)

\(\text{Therefore,}\)

\(\int x^2 6^{x^3+8}dx=\frac{6^{x^3+8}}{3\ln(6)}\)