Integral of : cosx dx. = ——————— [cosx/2 +sinx/2]^5
Integral of : cosx dx. =
———————
[cosx/2 +sinx/2]^5
Myra , 6 Years ago
Grade 11
Integral Calculus> Integral of : cosx dx. = ——————— [cosx/2 ...
1 AnswersMyra
Let cosx= (cosx/2-sinx/2)(cosx/2+sinx/2)
After substituting
∫(cosx/2-sinx/2) dx
——————————
(cosx/2+sinx/2)^4
Let (cosx/2+sinx/2) = t
By differentiating
[cosx/2 - sinx/2] dx= 2dt
After substitution
2∫dt
——— =
t^4
After integration
-2/3( t^-3) + C
-2/3 [ sinx/2 +cosx/2]^-3 +C
t^4
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