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October 20, 2014

October 20, 2014

Posted by **mary** on Wednesday, May 5, 2010 at 2:08am.

integral of 4e^(4x)sin[e^(4x)]dx

- calculus -
**Damon**, Wednesday, May 5, 2010 at 4:59amlet y = 4 x

dy = 4 dx

so

integral of e^y sin y dy

try e^y cos y

derivative = -e^y sin y + e^y cos y

so

try ae^y cos y + be^y sin y

derivative = -ae^ysiny+ae^ycosy+be^ycosy+be^ysiny

we need a=-b to get rid of cos terms

so

-b e^y cos y +b e^y sin y

so

be^y sin y - be^y cos y

try derivative

b e^y cos y+be^y sin y+be^y siny-be^y cosy

=2 b e^y sin y

so let b = 1/2 and we are there

=(1/2)e^y [ sin y-cos y] + c

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