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Question
Integrate the following with respect to x:
x2 cos x
Solution
`int x^2 cos x "d"x`
u = x2
u' = 2x
u' = 2
u"' 0
dv = cos x dx
⇒ v= `int cos x "d"x`
= sin x
v1 = `int "v" "d"x`
= `int sinx "d"x`
= `- cos x`
v2 = `int "v"_1 "d"x`
= `int - cosx "d"x`
= `- sin x`
v3 = `int "v"_2 "d"x`
= `int- sin x "d"x`
= `- int sinx "d"x`
= `- (cos x)`
`int "u" "dv"` = uv – u'v1 + uv2 – u"'v3 + ...........
`int x^2 cos x "d"x = x^2 sin x - 2x xx cos x + 2 xx - sin x - 0 xx cos x + "c"`
`int x^2 cos x "d"x = x^2 sin x + 2x cosx - 2 sinx + "c"`
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