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is equal to
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a
−12cos(2x+1)+cos3(2x+1)6+C
b
−cos(2x+1)+13cos3(2x+1)+C
c
12cos(2x+1)−13cos3(2x+1)+C
d
None of the above
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Correct option is A
∫sin3(2x+1)dx=∫sin2(2x+1)⋅sin(2x+1)dx=∫1−cos2(2x+1)sin(2x+1)dx∵sin2x=1−cos2x Let cos(2x+1)=t⇒−2sin(2x+1)dx=dt⇒sin(2x+1)dx=−dt2∴∫sin3(2x+1)dx=−12∫1−t2dt=−12t−t33+C=−12cos(2x+1)−cos3(2x+1)3+C=−cos(2x+1)2+cos3(2x+1)6+CSimilar Questions
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