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What is the integral of the function f(x)=(x^2+1)^2?
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The indefinite integral of the function is the primitive function F(x), whose first derivative is the function f(x).
We need to expand the binomial first.
(x^2+1)^2 = x^4 + 2x^2 + 1
Now, we'll integrate both sides:
`int` (x^2+1)^2 dx = `int`(x^4 + 2x^2 + 1)dx
We'll use the property of integral to be additive:
`int` (x^4 + 2x^2 + 1)dx = `int` x^4 dx + `int` 2x^2 dx + `int` dx
`int` (x^4 + 2x^2 + 1)dx = x^5/5 + 2x^3/3 + x + C
The requested value of the indefinite integral of the given function is F(x) = x^5/5 + 2x^3/3 + x + C.
Posted by giorgiana1976 on August 2, 2011 at 10:47 PM (Answer #1)
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