Evaluate the following integrals. int x^2 6^{x^3+8}dx

Question
Integrals
Evaluate the following integrals.
$$\int x^2 6^{x^3+8}dx$$

2021-02-01
We have given
$$\int x^2 6^{x^3+8}dx$$
$$\text{Take }x^2 6^{x^3+8}$$
$$\Rightarrow 3x^2dx=dt$$
$$\Rightarrow x^2dx=\frac{dt}{3}$$
$$\text{Then,}$$
$$\int x^2 6^{x^3+8}=\frac{1}{3}\int6^tdt$$
$$=\frac{1}{3}\frac{6^t}{\ln(6)}$$
$$=\frac{1}{3}\cdot\frac{6^{x^3+8}}{\ln(6)}$$
$$=\frac{6^{x^3+8}}{3\ln(6)}$$
$$\text{Therefore,}$$
$$\int x^2 6^{x^3+8}dx=\frac{6^{x^3+8}}{3\ln(6)}$$

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