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x-3-x-2-2x-3-dx-




Question Number 204866 by mathlove last updated on 29/Feb/24
∫ ((x+3)/(x^2 (√(2x+3)))) dx=?
$$\int\:\frac{{x}+\mathrm{3}}{{x}^{\mathrm{2}} \sqrt{\mathrm{2}{x}+\mathrm{3}}}\:{dx}=? \\ $$
Answered by Frix last updated on 29/Feb/24
∫((x+3)/(x^2 (√(2x+3))))dx =^(t=((√(2x+3))/x)) −∫dt=−t=−((√(2x+3))/x)+C
$$\int\frac{{x}+\mathrm{3}}{{x}^{\mathrm{2}} \sqrt{\mathrm{2}{x}+\mathrm{3}}}{dx}\:\overset{{t}=\frac{\sqrt{\mathrm{2}{x}+\mathrm{3}}}{{x}}} {=}−\int{dt}=−{t}=−\frac{\sqrt{\mathrm{2}{x}+\mathrm{3}}}{{x}}+{C} \\ $$

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