7.1 Integration By Parts/53: Difference between revisions

Revision as of 12:38, 13 December 2022

$y=xe^{-0.4x}~~~x=0,x=1$

$\underbrace {\int _{0}^{5}xe^{-0.4x}dx}$

${\begin{aligned}u&=x\quad dv=e^{-x}dx\\[2ex]du&=2xdx\qquad v=-e^{-x}\\[2ex]\end{aligned}}$

@@ Line 1: / Line 1: @@
 <math>y= xe^{-0.4x} ~~~ x=0,x=1</math>
-<math> \underbrace{\int_{0}^{5}xe^{-0.4x}dx}
+<math> \underbrace{\int_{0}^{5}xe^{-0.4x}dx} </math>
-\begin{aligned}
+<math>
-u & = \ln^{2}{(x)}  & dv &= dx \\[0.6ex]
+\begin{align}
-du & = \tfrac{2\ln{(x)}}{x}dx  & v &= x
+u &= x \quad dv= e^{-x}dx \\[2ex]
-\end{aligned}} \\ [2ex]\end
+du &= 2xdx        \qquad v= -e^{-x} \\[2ex]
+\end{align}
 </math>