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Please i need step by step explanation on how to integrate 3x^{4} - 4x^{-3} with respect to x

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First, you need to know the general rule of integration:

x^{n} = x^{n+1}/n+1

Using this integration rule for your question, 3x^{4} - 4x^{-3}, will become:

3x^{4+1}/4+1 - 4x^{-3+1}/-3+1

It becomes:

4x^{5}/5 - 4x^{-2}/-2

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