MAC 2312 Lecture 4: 7.1 Integration by parts
20 Jun 2018
School
Department
Course
Professor
5121118
Integration by parts Monday
Example : Find )|n ×dx
Soln ;
fcx ) = In ×of
' (x)=/
fi (×) =tz g(×)-×
Slnxdx = xinx -fly × dx
= tsnx -
51 dx
= xlnx -X + C
Example :Stan
''
xdx
Soln :
f ( ×)-+ an
- ' ×glcx ) = 1
f '(×)= 1
1 + ×2 ,
GC×)=×
)t an
''
d x = xtan
' '
×-g¥e×DX
= x + an
' '
x -tz f2×-2 dx
ltx
= × t an
-'x -tz in ((+ ×2 )+(
Example ! Find Set sin ×DX
Solh :
fcx )= sinx g
'
C×)=
e
×
ficx ) =
cosx
g
(×)= e
+
Set sin xdx =
etsinx -5cos × et d ×
f ( ×)= cos ×of 1 C×) = ex
fix )=-sin ×of C×)= et
Scos etdx = e
→
cost -gfs ;n×\e×dx
= e× cosx +Ssinx e× dx
)e× Sinxdx =e
×sinx -excosx -SSin ×e×d×
25 e×Sinxdx = e× sins -excos × + (so tz Of -"
