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2-4-2x-2-1-1-x-2-2-dx-




Question Number 186194 by normans last updated on 02/Feb/23
        ∫_2 ^4   ((2x^2  − 1)/(1 +  (√x^2 )  −  2))  dx
$$ \\ $$$$\:\:\:\:\:\:\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\:\:\frac{\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} \:−\:\mathrm{1}}{\mathrm{1}\:+\:\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} }\:\:−\:\:\mathrm{2}}\:\:\boldsymbol{{dx}}\:\:\:\: \\ $$$$ \\ $$
Commented by MJS_new last updated on 02/Feb/23
(√x^2 ) why not x?
$$\sqrt{{x}^{\mathrm{2}} }\:\mathrm{why}\:\mathrm{not}\:{x}? \\ $$
Commented by mr W last updated on 02/Feb/23
i don′t think this guy is serious or  really interested in mathemstics,  when he writes things like 1+(√x^2 )−2.  maybe he just composes questions   with some mathematical symbols,  no matter whether it makes sense or  not.
$${i}\:{don}'{t}\:{think}\:{this}\:{guy}\:{is}\:{serious}\:{or} \\ $$$${really}\:{interested}\:{in}\:{mathemstics}, \\ $$$${when}\:{he}\:{writes}\:{things}\:{like}\:\mathrm{1}+\sqrt{{x}^{\mathrm{2}} }−\mathrm{2}. \\ $$$${maybe}\:{he}\:{just}\:{composes}\:{questions}\: \\ $$$${with}\:{some}\:{mathematical}\:{symbols}, \\ $$$${no}\:{matter}\:{whether}\:{it}\:{makes}\:{sense}\:{or} \\ $$$${not}. \\ $$
Answered by MJS_new last updated on 02/Feb/23
∫_2 ^4 ((2x^2 −1)/(1+(√x^2 )−2))dx=[x^2 +2x+ln ∣x−∣]_2 ^4 =16+ln 3
$$\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\frac{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{1}}{\mathrm{1}+\sqrt{{x}^{\mathrm{2}} }−\mathrm{2}}{dx}=\left[{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{ln}\:\mid{x}−\mid\right]_{\mathrm{2}} ^{\mathrm{4}} =\mathrm{16}+\mathrm{ln}\:\mathrm{3} \\ $$

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