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education/math/MATH1220 (calc II)/Integration by Parts.md

@@ -17,4 +17,8 @@ Now, let $u = f(x)$ and $v = g(x)$, then $dv = g'(x)dx$ and $du = f'(x)dx$.
 # Examples
 >  Evaluate the below antiderivative using integration by parts.
 $$\int xe^{2x}dx$$
-1. Define $u$ to be a value you can take the derivative of easily, in this case $u = x$, 
+1. Define $u$ to be a value you can take the derivative of easily, in this case $u = x$. The rest of the integral will be set to $dv$, in this case, $dv = e^{2x}dx$. 
+	- $u = x$
+	- $du = \frac{d}{dx}(x)= 1dx$ 
+	- $dv = e^{2x}dx$
+	- $v = \frac{1}{2}e^{2x}$ - The antiderivative of $dv$.