Mathematics

$$\displaystyle\int{\dfrac{1+\cos{x}}{x+\sin{x}}dx}$$


SOLUTION
Let $$t=x+\sin{x}\Rightarrow dt=\left(1+\cos{x}\right)dx$$
$$\displaystyle\int{\dfrac{1+\cos{x}}{x+\sin{x}}dx}$$
$$=\displaystyle\int{\dfrac{dt}{t}}$$
$$=\log{t}+c$$
$$=\log{\left(x+\sin{x}\right)}+c$$ where $$c$$ is the constant of integration.

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Subjective Medium Published on 17th 09, 2020
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