Find the antiderivative of 
| Foundations:
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| This problem requires two rules of integration, integration by substitution (U - sub) and the power rule.
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| Additionally, we will need our power rule for integration:
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- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int x^{n}dx\,=\,{\frac {x^{n+1}}{n+1}},}
for
 ,
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Solution:
| Step 1:
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Use a U-substitution with Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle u = 3x + 2.}
This means Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle du = 3 dx}
, and after substitution we have
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \left(3x + 2\right)^4 dx = \int u^4 du}
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| Step 2:
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We can no apply the power rule for integration:
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int u^4 du = \frac{u^5}{5}}
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| Step 3:
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| Since our original function is a function of x, we must substitute x back into the result from problem 2:
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- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{u^5}{5} = \frac{(3x + 2)^5}{5}}
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| Step 4:
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| As will all indefinite integrals, don't forget the "+C" at the end.
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| Final Answer:
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| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int \left(3x + 2\right)^5 dx\,=\, \frac{(3x + 2)^5}{5} + C}
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