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

@@ -7,5 +7,11 @@ $$ \frac{d}{dx}(f(x)g(x)) = f'(x)g(x) + f(x)g'(x) $$
 $$\int \frac{d}{dx} (f(x)g(x))dx = \int [f'(x)g(x) + f(x)]$$
 2. Through the distributive property of integrals,
 $$ = \int f'(x)g(x)dx + \int f(x)g'(x)dx $$
-3. Therefore:
-$$f(x)g(x) = \intf'(x)g(x)dx $$
+3. An integral cancels out an antiderivative, therefore:
+$$f(x)g(x) = \int f'(x)g(x)dx + \int f(x)g'(x)dx $$
+4. Moving terms around:
+$$ \int f(x)g'(x)dx = f(x)g(x) - \int f'(x)g(x)dx$$
+
+Now, let $u = f(x)$ and $v = g(x)$, then $dv = g'(x)dx$ and $du = f'(x)dx$. 
+
+# Examples