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Find-x-4-x-3-dx-




Question Number 207129 by hardmath last updated on 07/May/24
Find:     ∫ ((x + 4)/(x + 3)) dx = ?
$$\mathrm{Find}:\:\:\:\:\:\int\:\frac{\mathrm{x}\:+\:\mathrm{4}}{\mathrm{x}\:+\:\mathrm{3}}\:\mathrm{dx}\:=\:? \\ $$
Answered by mathzup last updated on 08/May/24
∫((x+4)/(x+3))dx=∫((x+3+1)/(x+3))dx =∫dx +∫(dx/(x+3))  =x+ln∣x+3∣ +c
$$\int\frac{{x}+\mathrm{4}}{{x}+\mathrm{3}}{dx}=\int\frac{{x}+\mathrm{3}+\mathrm{1}}{{x}+\mathrm{3}}{dx}\:=\int{dx}\:+\int\frac{{dx}}{{x}+\mathrm{3}} \\ $$$$={x}+{ln}\mid{x}+\mathrm{3}\mid\:+{c} \\ $$

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