求定积分，我跪了，求大神拯救，题目见图？
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I = ∫<-1, 1>2x^2dx/[1+√(1-x^2)] + ∫<-1, 1>xcosxdx/[1+√(1-x^2)]
= 4∫<0, 1>x^2dx/[1+√(1-x^2)] + 0, 令 x = sint
I = 4∫<0, π/2>(sint)^2 costdt/(1+cost)
= 4∫<0, π/2>(1-cost)costdt = 4∫<0, π/2>[cost-(cost)^2]dt
= 2∫<0, π/2>[2cost-1-cos2t]dt
= 2[2sint-t-(1/2)sin2t]<0, π/2> = 4-π
= 4∫<0, 1>x^2dx/[1+√(1-x^2)] + 0, 令 x = sint
I = 4∫<0, π/2>(sint)^2 costdt/(1+cost)
= 4∫<0, π/2>(1-cost)costdt = 4∫<0, π/2>[cost-(cost)^2]dt
= 2∫<0, π/2>[2cost-1-cos2t]dt
= 2[2sint-t-(1/2)sin2t]<0, π/2> = 4-π
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