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Indefinite Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIndefinite Integrals2 Marks
Question
Evaluate $\int\frac{\text{x}^3-\text{x}^2+\text{x}+1}{\text{x}-1}\text{ dx}$
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Answer

Let $\text{I}=\int\frac{\text{x}^3-\text{x}^2+\text{x}+1}{\text{x}-1}\text{ dx}$
$=\int\frac{\text{x}^2(\text{x}-1)+(\text{x}-1)}{(\text{x}-1)}\text{ dx}$
$=\int\text{x}^2\text{dx}+\int\text{dx}$
$=\frac{\text{x}^3}{3}+\text{x}+\text{C}$

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