# What is the integral of #int 1/(x^3-1) dx#?

Here,

Take,

So,

#=1/3ln|x- 1|-1/6ln(x^2+x+1)-1/2xx1/(sqrt3/2)tan^-1((x+1/2)/(sqrt3/2))+c#

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The integral of ( \frac{1}{x^3 - 1} ) with respect to ( x ) is given by:

[ \int \frac{1}{x^3 - 1} , dx = \frac{1}{3} \ln\left|\frac{x - 1}{x^2 + x + 1}\right| + 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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