# How do you find the indefinite integral of #int (x^2+1)^3dx#?

Expand the integrand and integrate term-by-term.

So

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To find the indefinite integral of ( \int (x^2+1)^3 , dx ), we can use the substitution method.

Let ( u = x^2 + 1 ). Then, ( du = 2x , dx ).

Rewriting the integral in terms of ( u ), we get:

[ \int u^3 , du ]

Integrating ( u^3 ) with respect to ( u ), we get:

[ \frac{u^4}{4} + C ]

Now, substituting back ( u = x^2 + 1 ), we have:

[ \frac{(x^2 + 1)^4}{4} + C ]

Therefore, the indefinite integral of ( \int (x^2+1)^3 , dx ) is ( \frac{(x^2 + 1)^4}{4} + C ), where ( C ) is the constant of integration.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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