# How do you integrate #f(x)=x(x^7+15)^3# using the product rule?

You must have meant to differentiate, as the product rule does not allow for integration.

Apply the product rule, which specifies

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To integrate ( f(x) = x(x^7 + 15)^3 ) using the product rule, first, let ( u = x ) and ( v = (x^7 + 15)^3 ). Then, apply the product rule which states that ( \int u \cdot v , dx = \int u , dv + \int v , du ). Differentiate ( u ) to get ( du ) and integrate ( v ) to get ( dv ). After that, substitute the values into the formula and integrate each part separately. Finally, combine the results to obtain the integral of the original function.

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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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