Evaluate the Integral

[sunkist]

My problem is, I don't understand where the 77/81 is coming from: Steps shown are greatly appreciated.
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Problem -> Evaluate the integral: integral sign(sin2xcos9x)dx




integral sign (sin2xcos9x)dx = (1/9)sin2xsin9x+ (2/81)cos2xcos9x + (4/81)integral sign(sin2xcos9x)dx

simplify:

(77/81) integral sign(sin2xcos9x)dx = (1/9)sin2xsin9x+(2/81)cos2xcos9x

final answer: 9/77 sin2xsin9x + 2/77cos2xcos9x+C

 

[Ishuda]

My problem is, I don't understand where the 77/81 is coming from: Steps shown are greatly appreciated.
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Problem -> Evaluate the integral: integral sign(sin2xcos9x)dx




integral sign (sin2xcos9x)dx = (1/9)sin2xsin9x+ (2/81)cos2xcos9x + (4/81)integral sign(sin2xcos9x)dx

simplify:

(77/81) integral sign(sin2xcos9x)dx = (1/9)sin2xsin9x+(2/81)cos2xcos9x

final answer: 9/77 sin2xsin9x + 2/77cos2xcos9x+C

You have a
I = (1/9) a + (2/81) b + (4/81) I
or
(1 - 4/81) I = 1/9 a + 2/81 b