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What is the antiderivative of the function f(x) given by f(x)=x*e^8x ?
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We'll integrate by parts, according to the identity below:
Int udv = u*v - Int vdu (*)
We'll put u = x. (1)
We'll differentiate both sides:
du = dx (2)
We'll put dv = e^8x (3)
We'll integrate both sides:
Int dv = Int e^8x dx
v = e^8x/8 (4)
We'll substitute (1) , (2) , (3) and (4) in the formula (*):
Int udv = x*e^8x/8 - Int (e^8x/8)dx
Int (x*e^8x)dx = x*e^8x/8 - e^8x/64 + C
Posted by giorgiana1976 on April 13, 2011 at 9:27 PM (Answer #1)
The antiderivative of f(x)=x*e^8x can be found using integration by parts.
Int [u dv ]= u*v - Int[ v du]
Let u = x => du = 1
dv = e^8x => v = e^8x/8
Int [ x*e^8x ] = (x*e^8x)/8 - Int [1*(e^8x)/8]
=> (x*e^8x)/8 - (e^8x)/64
The anti-derivative is (x*e^8x)/8 - (e^8x)/64 + C
Posted by justaguide on April 13, 2011 at 9:37 PM (Answer #2)
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