. ∫(cos5x + cos4x)/(1-2cos3x) dx is equal to : how to solve
. ∫(cos5x + cos4x)/(1-2cos3x) dx is equal to : how to solve
ABHAY SHANKAR , 14 Years ago
Grade 12
Integral Calculus> ic...
1 Answers
SAGAR SINGH - IIT DELHI
Last Activity: 14 Years ago
Dear student,,
given integral
=2(cos9x/2cosx/2)/1-2(2cos23x/2-1) dx
now multiply and divide by cos3x/2
=2(cosx/2cos3x/2cos9x/2)/(3cos3x/2-4cos33x/2)dx
=2(cosx/2cos3x/2cos9x/2)/-cos9x/2 dx
=-2cosx/2cos3x/2 dx
= -(cos2x+cosx)dx
therefore the answer is -sin2x/2 - sinx
=2(cos9x/2cosx/2)/1-2(2cos23x/2-1) dx
now multiply and divide by cos3x/2
=2(cosx/2cos3x/2cos9x/2)/(3cos3x/2-4cos33x/2)dx
=2(cosx/2cos3x/2cos9x/2)/-cos9x/2 dx
=-2cosx/2cos3x/2 dx
= -(cos2x+cosx)dx
therefore the answer is -sin2x/2 - sinx
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