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x+sinxOr, Evaluated1+ cosx |
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Answer» ∫ ( x + sin(x)) dx /(1 + cos(x) = ∫ ( x + 2sin(x/2)cos(x/2)) dx /(1 + 2cos^2(x/2) - 1) = ∫ ( x + 2sin(x/2)cos(x/2)) dx / 2cos^2(x/2) = ∫ x dx / 2 cos^2(x/2) + ∫ tan(x/2) dx = 1/2∫ x sec^2(x/2) dx + ∫ tan(x/2) dx --------------------(1) integrate first integral by partsu = xdu = dx dv = (1/2)sec^2(x/2) dxv = tan(x/2) 1/2∫ x sec^2(x/2) dx = x tan(x/2) - ∫ tan(x/2) dx substitute in (1) 1/2∫ x sec^2(x/2) dx + ∫ tan(x/2) dx = x tan(x/2) - ∫ tan(x/2) dx + ∫ tan(x/2) dx = x tan(x/2) + C send pictures |
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