AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

This commit is contained in:
Christoph J. Scherr 2024-09-06 17:21:12 +02:00
parent 595773d2fe
commit 02145437cd
Signed by: cscherrNT
GPG Key ID: 8E2B45BC51A27EA7
2 changed files with 24 additions and 0 deletions

Binary file not shown.

View File

@ -169,3 +169,27 @@ $
&= sin(u) \ &= sin(u) \
&= sin(ln(x)) \ &= sin(ln(x)) \
$ $
#pagebreak()
=== Exercise 5 @Exercise[1, 5]
#block(
fill: luma(230),
inset: 8pt,
radius: 4pt,
[
Calculate the following integrals using partial integration:
#set enum(numbering: "(a)")
+ $ integral (x+2) dot e^(2x) d x $
+ $ integral x^2 dot ln(x) d x $
])
#set enum(numbering: "(a)")
+ $
A &= integral (x+2) dot e^(2x) d x \
&= integral u(x) dot v'(x) d x \
&= u(x) dot v(x) - integral u'(x) dot v(x) d x \
&= (x+2) dot (e^(2x) dot 1/2x) - integral e^(2x) d x \
&= (x+2) dot (e^(2x) dot 1/2x) - e^(2x) dot 1/2x \
&= x dot (e^(2x) dot 1/2x) + e^(2x) dot 1/2x \
$