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Questions
Find the following integrals:
`int (x^3 - x^2 + x - 1)/(x - 1) dx`
Evaluate:
`int (x^3 - x^2 + x - 1)/(x - 1) dx`
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Solution
Given: `int (x^3 - x^2 + x - 1)/(x - 1) dx`
= `int (x^2 (x - 1) + 1(x - 1))/((x - 1)) dx`
= `int ((x - 1) (x^2 + 1))/((x - 1)) dx`
= `int (x^2 + 1) dx`
= `int x^2 dx + int 1 dx`
= `x^3/3 + x + c`
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