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∫ Sin 2 ( 2 X + 5 ) D X - Mathematics

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Question

\[\int \text{sin}^2 \left( 2x + 5 \right) \text{dx}\]

Sum

Solution

\[\int \text{sin}^2 \left( 2x + 5 \right) \text{dx}\]
\[ = \int\left( \frac{1 - \cos \left( 4x + 10 \right)}{2} \right)dx \left[ \therefore \sin^2 A = \frac{1 - \cos2A}{2} \right]\]
\[ = \frac{1}{2}\int\left( 1 - \cos \left( 4x + 10 \right) \right)dx\]
\[ = \frac{1}{2}\left[ x - \frac{\sin \left( 4x + 10 \right)}{4} \right] + C\]
\[ = \frac{1}{2}x - \frac{\sin \left( 4x + 10 \right)}{8} + C\]

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Indefinite Integral Problems

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Chapter 19: Indefinite Integrals - Exercise 19.06 [Page 36]

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RD Sharma Mathematics [English] Class 12

Chapter 19 Indefinite Integrals
Exercise 19.06 | Q 1 | Page 36

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