Mathematics

Mathematics

Problem

Suppose J=∫sin⁡2x+sin⁡x1+sin⁡x+cos⁡x dxJ = \int \frac{\sin^2 x + \sin x}{1 + \sin x + \cos x}\,dx and K=∫cos⁡2x+cos⁡x1+sin⁡x+cos⁡x dxK = \int \frac{\cos^2 x + \cos x}{1 + \sin x + \cos x}\,dx. If CC is an arbitrary constant of integration then which of the following is/are correct? (a) J=12(x−sin⁡x+cos⁡x)+CJ = \frac{1}{2}(x - \sin x + \cos x) + C (b) J=K−(sin⁡x+cos⁡x)+CJ = K - (\sin x + \cos x) + C (c) J=x−K+CJ = x - K + C (d) K=12(x−sin⁡x+cos⁡x)+CK = \frac{1}{2}(x - \sin x + \cos x) + C (a) J=12(x−sin⁡x+cos⁡x)+CJ = \frac{1}{2}(x - \sin x + \cos x) + C (b) J=K−(sin⁡x+cos⁡x)+CJ = K - (\sin x + \cos x) + C (c) J=x−K+CJ = x - K + C (d) K=12(x−sin⁡x+cos⁡x)+CK = \frac{1}{2}(x - \sin x + \cos x) + C

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