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Question Number 167145 by mkam last updated on 07/Mar/22

$$\int \frac{dx}{x^2-3\sqrt{x}+10}$$

Commented by MJS_new last updated on 07/Mar/22

$$1^{\mathrm{st}}\mathrm{step}t=\sqrt{x}\to dx=2tdt\Rightarrow$$$$2\int \frac{t}{t^4-3t+10}dt$$$$\mathrm{but}\mathrm{we}\mathrm{cannot}\mathrm{get}\mathrm{the}\mathrm{roots}\mathrm{exactly}\Rightarrow \mathrm{we}$$$$\mathrm{cannot}\mathrm{solve}\mathrm{it}\mathrm{exactly}.$$$$2\int \frac{t}{t^4-3t+10}dt=\int \frac{At+B}{t^2-\alpha t-\beta }dt+\int \frac{Ct+D}{t^2+\alpha t-\gamma }dt$$$$\mathrm{these}\mathrm{can}\mathrm{be}\mathrm{solved}\mathrm{by}\mathrm{using}\mathrm{the}\mathrm{common}$$$$\mathrm{formula}\mathrm{but}\mathrm{all}\mathrm{the}\mathrm{constants}\mathrm{are}\mathrm{not}\mathrm{exact}$$$$\mathrm{numbers}$$

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