# How do you evaluate the integral #int (lnx)^3dx#?

Substitute:

so:

Integrate now by parts:

Putting it all together:

and undoing the substitution:

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To evaluate the integral ∫(lnx)^3 dx, you can use integration by parts. Let u = (lnx)^3 and dv = dx. Then, differentiate u and integrate dv to find du and v respectively. After that, apply the integration by parts formula:

∫u dv = uv - ∫v du

Finally, substitute the values of u, v, du, and dv into the formula and solve the integral.

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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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