diff --git a/education/math/MATH1220 (calc II)/Integration by Parts.md b/education/math/MATH1220 (calc II)/Integration by Parts.md index 10112ea..0f706f2 100644 --- a/education/math/MATH1220 (calc II)/Integration by Parts.md +++ b/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 $u = x$, \ No newline at end of file +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 $dv$. \ No newline at end of file