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  • Evaluate the following: \int \frac{(1 plus \cos x)}{x plus \sin x} d x

Evaluate the following:

\int \frac{(1+\cos x)}{x+\sin x} d x

Answers (1)

Given; \int \frac{(1+\cos x)}{x+\sin x} d x

Let t = x + sin x



\\\Rightarrow dt = (1 + cos x) dx \\ =\int \frac{1}{t} d t \\ =\log |t|+C \\ =\log |x+\sin x|+C

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