（1）原式=∫√x*2√xd(√x)/(1+x) (dx=2√xd(√x))
=2∫[1-1/(1+(√x)²)]d(√x)
=2[√x-arctan(√x)]│
=2(1-π/4)
=2-π/2；
（3）原式=∫(sint)^4*cost*costdt (令x=sint)
=(1/8)∫[(1-cos(2t))/2][sin²(2t)/4]dt (应用倍角公式)
=(1/8)∫[1/2-cos(4t)/2-cos(2t)sin²(2t)]dt (再次应用倍角公式)
=(1/8)[t/2-sin(4t)/8-sin³(2t)/6]│
=(1/8)(π/2)/2
=π/32.