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

Question
Integrals
asked 2021-01-31
Evaluate the following integrals.
\(\int x^2 6^{x^3+8}dx\)

Answers (1)

2021-02-01
We have given
\(\int x^2 6^{x^3+8}dx\)
\(\text{Take }x^2 6^{x^3+8}\)
\(\Rightarrow 3x^2dx=dt\)
\(\Rightarrow x^2dx=\frac{dt}{3}\)
\(\text{Then,}\)
\(\int x^2 6^{x^3+8}=\frac{1}{3}\int6^tdt\)
\(=\frac{1}{3}\frac{6^t}{\ln(6)}\)
\(=\frac{1}{3}\cdot\frac{6^{x^3+8}}{\ln(6)}\)
\(=\frac{6^{x^3+8}}{3\ln(6)}\)
\(\text{Therefore,}\)
\(\int x^2 6^{x^3+8}dx=\frac{6^{x^3+8}}{3\ln(6)}\)
0

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