求不定积分∫e^3xcos2xdx ∫arccotxdx
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∫e^3xcos2xdx=(1/3)∫cos2xde^(3x)
= (1/3) (cos3x) e^(3x) +(2/3)∫ (sin2x)e^(3x)dx
= (1/3) (cos3x) e^(3x) +(2/9)∫ (sin2x)de^(3x)
=(1/3) (cos3x) e^(3x) +(2/9)(sin2x)e^(3x) - (4/9)∫ (cos2x)e^(3x) dx
(13/9)∫e^3xcos2xdx = (1/3) (cos3x) e^(3x) +(2/9)(sin2x)e^(3x) + C'
∫e^3xcos2xdx = (9/13) [ (1/3) (cos3x) e^(3x) +(2/9)(sin2x)e^(3x) ] = C
∫arccotxdx
= xarccotx - ∫ x/√(1+x^2) dx
= xarccotx - √(1+x^2) + C
= (1/3) (cos3x) e^(3x) +(2/3)∫ (sin2x)e^(3x)dx
= (1/3) (cos3x) e^(3x) +(2/9)∫ (sin2x)de^(3x)
=(1/3) (cos3x) e^(3x) +(2/9)(sin2x)e^(3x) - (4/9)∫ (cos2x)e^(3x) dx
(13/9)∫e^3xcos2xdx = (1/3) (cos3x) e^(3x) +(2/9)(sin2x)e^(3x) + C'
∫e^3xcos2xdx = (9/13) [ (1/3) (cos3x) e^(3x) +(2/9)(sin2x)e^(3x) ] = C
∫arccotxdx
= xarccotx - ∫ x/√(1+x^2) dx
= xarccotx - √(1+x^2) + C
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