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Question Number 90110 by jagoll last updated on 21/Apr/20

∫_((2/3)u) ^(2u)  (e^(−(x/2)) /(2π (√((u−(1/2)x)(((3x)/2)−u))))) du   (u > 0 )

$$\underset{\frac{\mathrm{2}}{\mathrm{3}}\mathrm{u}} {\overset{\mathrm{2u}} {\int}}\:\frac{\mathrm{e}^{−\frac{\mathrm{x}}{\mathrm{2}}} }{\mathrm{2}\pi\:\sqrt{\left(\mathrm{u}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\right)\left(\frac{\mathrm{3x}}{\mathrm{2}}−\mathrm{u}\right)}}\:\mathrm{du}\: \\ $$ $$\left(\mathrm{u}\:>\:\mathrm{0}\:\right) \\ $$

Commented byMJS last updated on 21/Apr/20

dependent borders are not allowed  ∫_(f(x)) ^(g(x)) h(x)dx simply makes no sense

$$\mathrm{dependent}\:\mathrm{borders}\:\mathrm{are}\:\mathrm{not}\:\mathrm{allowed} \\ $$ $$\underset{{f}\left({x}\right)} {\overset{{g}\left({x}\right)} {\int}}{h}\left({x}\right){dx}\:\mathrm{simply}\:\mathrm{makes}\:\mathrm{no}\:\mathrm{sense} \\ $$

Commented byabdomathmax last updated on 21/Apr/20

you are right sir.

$${you}\:{are}\:{right}\:{sir}. \\ $$

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