∫ Sec − 1 √ X D X - Mathematics

Question

\[\int \sec^{- 1} \sqrt{x}\ dx\]

Sum

Solution

\[\int 1_{II} . \sec^{- 1} \sqrt{x}_I dx\]
\[ = \sec^{- 1} \sqrt{x}_{} \int1\text{ dx }- \int\left\{ \frac{d}{dx}\left( \sec^{- 1} \sqrt{x} \right)\int1 \text{ dx }\right\}dx\]
\[ = \sec^{- 1} \sqrt{x} . x - \int \frac{1}{\sqrt{x} \sqrt{1 - x}} \times \frac{1}{2\sqrt{x}} \times \text{ x dx }\]
\[ = x \sec^{- 1} \sqrt{x} - \frac{1}{2} \int \left( 1 - x \right)^{- \frac{1}{2}} dx\]
\[ = x \sec^{- 1} x - \frac{1}{2} \left[ \frac{\left( 1 - x \right)^{- \frac{1}{2} + 1}}{\left( - \frac{1}{2} + 1 \right) \left( - 1 \right)} \right] + C\]
\[ = x \sec^{- 1} x + \left( 1 - x \right)^\frac{1}{2} + C\]

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Indefinite Integral Problems

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Q 30 Q 29 Q 31

Chapter 19: Indefinite Integrals - Exercise 19.25 [Page 133]

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RD Sharma Mathematics [English] Class 12

Chapter 19 Indefinite Integrals
Exercise 19.25 | Q 30 | Page 133

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