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प्रश्न
Integrate the following with respect to x.
`(x^4 - x^2 + 2)/(x - 1)`
उत्तर
= `int(x^4 - x^2 + 2)/((x - 1)) "d"x`
= `int [(x^4 - xx^2)/((x - 1)) + 2/((x - 1))] "d"x`
= `int [(x^2(x^2 - 1))/((x - 1)) + 2/((x - 1))] "d"x`
= `int (x^2(x + 1)(x - 1))/((x - 1)) + 2/((x - 1))] "d"x`
= `int [(x^3 + x^2) + 2/((x - 1))] "d"x`
= `x^4/4 + x^3/3 + 2 log |x - 1| + "c"`
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