令x=√2sinβ,dx=√2cosβdβ(2-x²)^(3/2)=(2cos²β)^(3/2)=2√2cos³βcosβ=[(2-x²)^(3/2)/(2√2)]^(1/3)=√(2-x²)/√2∴∫(2-x²)^(3/2) dx=4∫cos⁴β dβ=4∫(cos²β)&s...
∫ √（2-x^2）^3dx 怎么积分求解.
令x=√2sinβ,dx=√2cosβdβ(2-x²)^(3/2)=(2cos²β)^(3/2)=2√2cos³βcosβ=[(2-x²)^(3/2)/(2√2)]^(1/3)=√(2-x²)/√2∴∫(2-x²)^(3/2) dx=4∫cos⁴β dβ=4∫(cos²β)&s...