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Evaluate of the Following Integral: ∫ 1 3 √ X 2 D X

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Question

Evaluate of the following integral:

\[\int\frac{1}{\sqrt[3]{x^2}}dx\]

Sum

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Solution

\[\int\frac{dx}{\sqrt[3]{x^2}}\]
\[ = \int\frac{dx}{x^{2/3}}\]
\[ = \int x^{- 2/3} dx\]
\[ = \frac{x^{- \frac{2}{3} + 1}}{- \frac{2}{3} + 1} + C\]
\[ = 3 x^\frac{1}{3} + C\]

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Evaluation of Definite Integrals

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Q 1.6 Q 1.5 Q 1.7

Chapter 18: Indefinite Integrals - Exercise 19.01 [Page 4]

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R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12

Chapter 18 Indefinite Integrals
Exercise 19.01 | Q 1.6 | Page 4

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