Mathematics

Integrate :  $$\dfrac{\cos \, x}{(1 - \sin \, x) (2 - \sin \, x)}$$


SOLUTION
$$\int \dfrac{\cos x}{(1-\sin x)(2-\sin x)}dx$$

substitute $$ u=1-\sin x\rightarrow du=-\cos x dx$$

$$\int -\dfrac{1}{u(u+1)}dx$$

$$-\left (  \int \dfrac{1}{u}-\dfrac{1}{u+1}du\right )$$

$$-(\ln u-\ln (u+1))$$

$$-\ln|1-\sin x|+\ln |2-\sin x|+C$$
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Subjective Medium Published on 17th 09, 2020
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