How do you integrate #int sinsqrtx# by parts?

1 Answer
Sonnhard
Jun 2, 2018

#2sqrt(x)*cos(sqrt(x))-2sin(sqrt(x))+C#

Explanation:

Substituting #t=sqrt(x)# then we get
#dx=2tdt#
and we have to solve
#2int tsin(t)dt#
By partial Integration we get
#int tsin(t)dt=tcos(t)-intcos(t)dt#
so we get
#2tcos(t)-2sin(t)+C#
#2sqrt(x)cos(sqrt(x))-2sin(sqrt(x))+C#

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