Make the given substitution to evaluate the indefinite integral. $$ \int 4(4x + 8)^7 dx, u = 4x + 8 $$
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Step 1
First, we need to find the differential $du$ in terms of $dx$. Given $u = 4x + 8$. Differentiate $u$ with respect to $x$: $$ \frac{du}{dx} = \frac{d}{dx}(4x + 8) $$ $$ \frac{du}{dx} = 4 $$ Now, we can write $du$ in terms of $dx$: $$ du = 4 dx $$ Step 2: Show more…
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