Integrate 2sinx cosx Tan -1 (sinx) dx Upper limit: pie/2 Lower Limit: 0
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2sinx cosx Tan -1 (sinx) = 2tanx cos^2x Tan -1 (sinx)
y = 2cos^2xsinx dx
t = cos^2x
dt = -2sinxcosxdx
dt = -y/cosx
-(√t)dt = y
integral y = integral -(√t)dt
= -(2/3)t^3/2
= -(2/3)cos^3x
limit 0 to pi/2
= 0 -(-2/3)
= 2/3
y = 2cos^2xsinx dx
t = cos^2x
dt = -2sinxcosxdx
dt = -y/cosx
-(√t)dt = y
integral y = integral -(√t)dt
= -(2/3)t^3/2
= -(2/3)cos^3x
limit 0 to pi/2
= 0 -(-2/3)
= 2/3
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