Evaluate $\int e^{9x-2}dx$ using $u$ substitution

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Section 5.3

Evaluate $\int e^{9x-2}dx$ using $u$ substitution.

Can somebody verify this for me? Thanks!


Let $u=9x-2$. Then $\frac{du}{dx}=9$ and so $\frac{du}{9}=dx$. Thus we have:

$\int e^{9x-2}dx$

$= \int e^u \frac{du}{9}$

$= \frac{1}{9} \int e^u du$

$=\frac{1}{9} e^u + C$

$=\frac{1}{9}e^{9x-2}+C$