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Integral of (x*arctg)sqrt2x-1 dx

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 |  \x*atan(x)*\/ 2*x  - 1/ dx
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$$\int\limits_{0}^{0} \left(\sqrt{2 x} x \operatorname{atan}{\left(x \right)} - 1\right)\, dx$$
Integral((x*atan(x))*sqrt(2*x) - 1, (x, 0, 0))
The answer (Indefinite) [src]
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 |                                         /              ___   ___\      /              ___   ___\         /      ___   ___\         /       ___   ___\       ___  3/2       ___  5/2        
 | /            _____    \              log\2 + 2*x + 2*\/ 2 *\/ x /   log\2 + 2*x - 2*\/ 2 *\/ x /   2*atan\1 + \/ 2 *\/ x /   2*atan\-1 + \/ 2 *\/ x /   4*\/ 2 *x      2*\/ 2 *x   *atan(x)
 | \x*atan(x)*\/ 2*x  - 1/ dx = C - x - ---------------------------- + ---------------------------- + ----------------------- + ------------------------ - ------------ + --------------------
 |                                                   5                              5                            5                         5                    15                 5          
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$$\int \left(\sqrt{2 x} x \operatorname{atan}{\left(x \right)} - 1\right)\, dx = C + \frac{2 \sqrt{2} x^{\frac{5}{2}} \operatorname{atan}{\left(x \right)}}{5} - \frac{4 \sqrt{2} x^{\frac{3}{2}}}{15} - x + \frac{\log{\left(- 2 \sqrt{2} \sqrt{x} + 2 x + 2 \right)}}{5} - \frac{\log{\left(2 \sqrt{2} \sqrt{x} + 2 x + 2 \right)}}{5} + \frac{2 \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{5} + \frac{2 \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{5}$$
The answer [src]
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Numerical answer [src]
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    Use the examples entering the upper and lower limits of integration.