du = \frac{dx}{\sqrt{1-x^2}}, dv = dx => v = x| = x*arcsinx - \int\limits^1_0 {\frac{x}{\sqrt{1-x^2}} } \, dx = x*arcsinx + \frac{1}{2} \int\limits^1_0 (1-x^2)^{-\frac{1}{2}} d(1-x^2) = x*arcsinx + \sqrt{1-x^2} = arcsin1 + 0 - 0 - 1 = \frac{\pi}{2} - 1\\ Answer: \frac{\pi}{2} - 1" alt="\int\limits^1_0 {arcsinx} \, dx = |u = arcsinx => du = \frac{dx}{\sqrt{1-x^2}}, dv = dx => v = x| = x*arcsinx - \int\limits^1_0 {\frac{x}{\sqrt{1-x^2}} } \, dx = x*arcsinx + \frac{1}{2} \int\limits^1_0 (1-x^2)^{-\frac{1}{2}} d(1-x^2) = x*arcsinx + \sqrt{1-x^2} = arcsin1 + 0 - 0 - 1 = \frac{\pi}{2} - 1\\ Answer: \frac{\pi}{2} - 1" align="absmiddle" class="latex-formula">