∫( Sin 6x+ Cos 6x+3 Sin 2x Cos 2x)dx Is Equal To - Tardigrade App

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4. ∫( sin 6x+ cos 6x+3 sin 2x cos 2x)dx is equal to

Q. ∫(sin6x+cos6x+3sin2xcos2x)dx is equal to 4926 165 KEAMKEAM 2007Integrals Report Error A

x+c

32% B

23​sin2x+c

15% C

−23​cos2x+c

14% D

31​sin3x−cos3x+c

25% E

31​sin3x+cos3x+c

25%

Solution:

Let I=∫(sin6x+cos6x+3sin2xcos2x)dx =∫{(sin2x)3+(cos2x)3 +3sin2xcos2x}dx} =∫[​(sin2x+cos2x)(sin4x+cos4x−sin2xcos2x)+3sin2xcos2x​]dx =∫[​(sin2x+cos2x)2−3sin2xcos2x+3sin2xcos2x​]dx =∫1dx =x+c