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Question Number 84126 by Roland Mbunwe last updated on 09/Mar/20

$$\int \frac{5-x}{1+\sqrt{(x-4)}}\mathit{d}\mathit{x}$$

Answered by MJS last updated on 09/Mar/20

$$-\int \frac{x-5}{1+\sqrt{x-4}}dx=\int (1-\sqrt{x-4})dx=$$$$=x-\frac{2}{3}{(x-4)}^{\frac{3}{2}}+C$$

Commented by MJS last updated on 09/Mar/20

$$-\frac{x-5}{1+\sqrt{x-4}}\times \frac{1-\sqrt{x-4}}{1-\sqrt{x-4}}=-\frac{(x-5)(1-\sqrt{x-4})}{5-x}=$$$$=1-\sqrt{x-4}$$

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