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Question Number 133440 by bagjagunawan last updated on 22/Feb/21

Answered by Ar Brandon last updated on 22/Feb/21

$$\mathrm{f}\left(x\right)=x+5+\sqrt{8x}+\sqrt{12x}+\sqrt{24}$$$$=x+(\sqrt{8}+\sqrt{12})\sqrt{x}+5+\sqrt{24}={(\sqrt{x}+\sqrt{2}+\sqrt{3})}^2$$$$\mathcal{I}=\int \mathrm{f}\left(x\right)\mathrm{d}x=\int \sqrt{{(\sqrt{x}+\sqrt{2}+\sqrt{3})}^2}\mathrm{d}x$$$$=\int (\sqrt{x}+\sqrt{2}+\sqrt{3})\mathrm{d}x=\frac{2}{3}\sqrt{x^3}+(\sqrt{2}+\sqrt{3})x+\mathcal{C}$$

Commented by bagjagunawan last updated on 22/Feb/21

$$\mathrm{Wow}$$$$\mathrm{thank}\mathrm{you}\mathrm{Sir}$$

Commented by Ar Brandon last updated on 22/Feb/21

You're welcome

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