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20.(cos2x)/((cos x+sin x)^(2))...

20.(cos2x)/((cos x+sin x)^(2))

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Integrate the functions (cos2x)/((cos x+sin x)^(2))

int(cos2x)/((cos x+sin x)^(2))dx

(i) int(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) dx

(i) int(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) dx

int(cos2x)/((sin x+cos x)^(2))dx=

(1 + sin 2x + cos 2x )/( cos x + sin x ) = 2 cos x

The value of (2(sin2x+2cos^(2)x-1))/(cos x sin x cos3x+sin3x) is

(cos^(3) x- sin^(2) x)/(cos x - sin x)=(1)/(2) (2 + sin 2x)

(cos2x)/(cos x-sin x)=cos x+sin x

int cos2x*log((cos x+sin x)/(cos x-sin x))backslash dx