- #1
bobsmith76
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Homework Statement
∫ x2 sin x
Homework Equations
uv - ∫ v du
The Attempt at a Solution
u = x2
du = 2x
dv = sin x
v = -cos x
step 1. x2 - cos x - ∫ -cos x 2x
I think -cos x * 2x becomes -2x cos x
so now we have
step 2. x2 - cos x - ∫ -2x cos x
which means I have to integrate by parts again. Here, concentrating on just the right hand side
u = 2x
du = 2
dv = cos x
v = sin x
step 3. 2x sin - ∫ sin x * 2
[after 10 minutes of research I've decided that I have to move that 2 to the left of the integral. That sort of helps. previously I took the antiderivative of 2.]
step 4. 2x sin + 2 -cosx
now add the left hand side part from above
step 5. x2 - cos x
step 6. x2 - cos x + 2x sin x + - 2 cosx + C
the book says the answer is
-x2 cos x + 2x sin x + 2 cos x + C
So I'm almost correct, I just don't understand how they got the negative on x2, Also my right cos x is negative and their's is positive.
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