What is the integral of the function f(x)=(x^2+1)^2?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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.