From 2cf8f820691ddbcb54c7d1ba0c9dcd285a76b233 Mon Sep 17 00:00:00 2001 From: arc Date: Wed, 3 Sep 2025 11:37:07 -0600 Subject: [PATCH] vault backup: 2025-09-03 11:37:07 --- education/math/MATH1220 (calc II)/Integration by Parts.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) 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