`int (x^3 - 8x)/x^2 dx` Find the indefinite integral.

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`int (x^3-8x)/x^2dx`

To solve, express the integrand as two fractions with same denominators.

`=int (x^3/x^2-(8x)/x^2)dx`

Simplify each fraction.

`=int (x - 8/x)dx`

Express it as difference of two integrals.

`=int xdx - int8/xdx`

For the first integral, apply the formula `intx^ndx= x^(n+1)/(n+1)+C` .

And for the second integral, apply the formula `int 1/xdx=ln|x|+C` .

`= int xdx - 8int1/xdx`

`=x^2/2-8ln|x|+C`

 

Therefore, `int (x^3-8x)/x^2dx = x^2/2-8ln|x|+C` .

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