Evaluate the following integrals.

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

Tazmin Horton
2021-01-31
Answered

Evaluate the following integrals.

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

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Cullen

Answered 2021-02-01
Author has **89** answers

We have given

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

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

$\Rightarrow 3{x}^{2}dx=dt$

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

$\text{Then,}$

$\int {x}^{2}{6}^{{x}^{3}+8}=\frac{1}{3}\int {6}^{t}dt$

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

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

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

$\text{Therefore,}$

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

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