用换元法求定积分,
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用换元法求定积分,
用换元法求定积分,
用换元法求定积分,
设 x = tant,则 dx = (sect)^2*dt.当 x = 0时,t = 0.当 x = 1时,t = π/4
∫dx/√(1+x^2)^3
=∫(sect)^2*dt/(sect)^3
=∫dt/(sect)
=∫cost*dt
=sint|0~π/4
=sin(π/4) - sin0
=√2/2