Integrate (x-x³)/x³ dx

Answer 1

We first split the fraction into two parts:

(x/x³) - (x³/x³)

The second term simplifies to:

1

For the first term, we can simplify the fraction by factoring out an x from the numerator:

x/x³ = 1/x²

So the integral becomes:

∫(1/x² - 1) dx

Integrating each term separately:

∫(1/x²) dx = -1/x

∫(-1) dx = -x

Putting it all together, the original integral is:

-1/x + (-x) + C

where C is the constant of integration.