[m] ∫^{sin1}_{0} \frac{(arcsinx)^2+1}{\sqrt{1-x^2}}dx= ∫^{sin1}_{0} \frac{(arcsinx)^2}{\sqrt{1-x^2}}dx+ ∫^{sin1}_{0} \frac{1}{\sqrt{1-x^2}}dx=[/m]
[m]=∫^{sin1}_{0} (arcsinx)^2d(arcsinx){\sqrt{1-x^2}}dx+ ∫^{sin1}_{0} \frac{1}{\sqrt{1-x^2}}dx=(\frac{(arcsinx)^3}{3}+arcsinx)|^{sin1}_{0}=\frac{1}{3}+1[/m]