Karnataka Board PUCPUC Science 2nd PUC Class 12

Evaluate: ∫ X 3 − 1 X 2 D X - Mathematics

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Sum

Evaluate:  \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]

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Solution

\[\int\left( \frac{x^3 - 1}{x^2} \right) dx\]
\[ = \int\left( \frac{x^3}{x^2} - \frac{1}{x^2} \right)dx\]
\[ = \int\left( x - x^{- 2} \right)dx\]
\[ = \frac{x^2}{2} - \frac{x^{- 2 + 1}}{- 2 + 1} + C\]
\[ = \frac{x^2}{2} + \frac{1}{x} + C\]

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Chapter 19: Indefinite Integrals - Very Short Answers [Page 198]

APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Very Short Answers | Q 48 | Page 198

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