# How do you find the indefinite integral of #int (12/x^4+8/x^5) dx#?

We can revert to positive exponents:

Thus,

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To find the indefinite integral of ( \int \left(\frac{12}{x^4} + \frac{8}{x^5}\right) , dx ), you can split it into two separate integrals:

- ( \int \frac{12}{x^4} , dx )
- ( \int \frac{8}{x^5} , dx )

For the first integral, use the power rule for integration:

[ \int \frac{12}{x^4} , dx = -\frac{12}{3x^3} + C = -\frac{4}{x^3} + C ]

For the second integral, also use the power rule for integration:

[ \int \frac{8

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