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integration of sin8x dx /(9+sin 4 x) 1/2 plz explain in detail


integration of sin8x dx /(9+sin4x)1/2


 


plz explain in detail


Grade:12

1 Answers

Rahul askIITiansExpert.IITR
110 Points
13 years ago
take sin2x=t

dt=2sinxcosxdx=sin2xdx

now the numerator of the expression: sin8xdx=2sin4xcos4xdx=4sin2xcos2xcos4xdx=4cos2xcos4xdt;

now we know that cos2x=cos2x-sin2x=1-2sin2x=1-2t

similarly, cos4x=1-sin22x=1-4sin2xcos2x=1-4t(1-t)=1-4t+4t2=4t2-2t-2t+1=(2t-1)2

the denominator is (9+t2)1/2

put the expressions in position

and expand the numerator

you will get different powers of t

separate than integrate each part separately

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