#160; #160; #160; #160; #160; #8747;sin2 #160;2x+5dx= #8747;1 cos #160;4x+102dx #160; #160; #160; #160; #160; #160; #160; #16 ...

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Monotonicity in an Interval

∫sin 22 x+5 d...

Question

$\int \sin^{2} (2 x + 5) d x$

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Solution

$\int \sin^{2} (2 x + 5) d x = \int (\frac{1 - \cos (4 x + 10)}{2}) d x [∴ \sin^{2} A = \frac{1 - \cos 2 A}{2}] = \frac{1}{2} \int (1 - \cos (4 x + 10)) d x = \frac{1}{2} [x - \frac{\sin (4 x + 10)}{4}] + C = \frac{1}{2} x - \frac{\sin (4 x + 10)}{8} + C$

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