(1)令x=sint,因x属于(-1,2),故t在(-pi/2,pi/2)内,且dx=costdt
∫x^2/根号(1-x^2)dx
=∫(sint)^2/cost×costdt
=∫(sint)^2 dt
=∫(1-cos2t)/2 dt
=t/2-sin2t/4+C
=arcsinx/2-x×根号(1-x^2)/2+C
(2)∫ln(1+x)dx
=∫ln(x+1)d(x+1)
=(x+1)ln(x+1)-∫(x+1)dln(x+1)
=(x+1)ln(x+1)-∫1 dx
=(x+1)ln(x+1)-x+C
(3)∫x*cos平方xdx
=∫x(1+cos2x)/2 dx
=∫x/2 dx+ ∫xcos2x/2 dx
=x^2/4+x sin2x/4-∫sin2x/4 dx
=x^2/4+x sin2x/4+cos2x/8 + C
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