Mathematics

Mathematics

Problem

∫cos⁡x(1+sin⁡x)(2+sin⁡x) dx=\int \frac{\cos x}{(1+\sin x)(2+\sin x)}\,dx = (a) log⁡[(1+sin⁡x)(2+sin⁡x)]+c\log\big[(1+\sin x)(2+\sin x)\big]+c (b) log⁡2+sin⁡x1+sin⁡x+c\log\frac{2+\sin x}{1+\sin x}+c (c) log⁡1+sin⁡x2+sin⁡x+c\log\frac{1+\sin x}{2+\sin x}+c (d) None of these (a) log⁡[(1+sin⁡x)(2+sin⁡x)]+c\log\big[(1+\sin x)(2+\sin x)\big]+c (b) log⁡2+sin⁡x1+sin⁡x+c\log\frac{2+\sin x}{1+\sin x}+c (c) log⁡1+sin⁡x2+sin⁡x+c\log\frac{1+\sin x}{2+\sin x}+c (d) None of these

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