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Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIntegrals1 Mark
Question
Evaluate: $\int \frac{x^3-x^2+x-1}{x-1} d x$
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Answer

$\text { (a) : Let } I=\int \frac{x^3-x^2+x-1}{x-1} d x$
$=\int \frac{x^2(x-1)+1(x-1)}{x-1}=\int \frac{\left(x^2+1\right)(x-1)}{x-1} d x$
$=\int\left(x^2+1\right) d x=\frac{1}{3} x^3+x+C$

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