企源知识库

求∫^1/2₀[(1-x)/√1-x²]dx
【正确答案】：∫^1/2₀[(1-x)/√1-x²]dx =∫^1/2₀[1/√(1-x²)]dx+1/2∫^1/2₀[d(1-x²)]/√(1-x²) =arcsinx∣^1/2₀+1/2×[1/-(1/2)+1](1-x²)^-(1/2)+1∣^1/2₀ =π/6+√(1-1/4)-√1=π/6+√3/2-1