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Question Number 86269 by M±th+et£s last updated on 27/Mar/20

$$\int \frac{{sec}^2\left(x\right)}{{(tan\left(x\right)-1)}^4(tan\left(x\right)-2)}dx$$

Commented by john santu last updated on 28/Mar/20

$$u=\tan x-2$$$$\Rightarrow \int \frac{du}{{(u+1)}^4\left(u\right)}$$$$decomposition$$$$\frac{1}{{(u+1)}^4\left(u\right)}=\frac{p}{u+1}+\frac{q}{{(u+1)}^2}+\frac{r}{{(u+1)}^3}$$$$+\frac{s}{{(u+1)}^4}+\frac{t}{u}$$$$$$

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