求定积分∫x²/(1-x²)½dx是不是要令x=sint?
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求定积分∫x²/(1-x²)½dx是不是要令x=sint?
求定积分∫x²/(1-x²)½dx
是不是要令x=sint?
求定积分∫x²/(1-x²)½dx是不是要令x=sint?
∫x²/√(1-x²)dx
=∫(x²-1+1)/√(1-x²)dx
=∫[-√(1-x²)+1/√(1-x²)]dx
=-1/2*x√(1-x^2)-1/2arcsinx+arcsinx+C
=-1/2*x√(1-x^2)+1/2arcsinx+C