高数：求下列的不定积分
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(3)
x^4
=x^2.(1+x^2) -x^2
=x^2.(1+x^2) -(1+x^2) +1
∫(0->1) x^4/(1+x^2)dx
=∫(0->1) [ x^2 -1 + 1/(1+x^2)]dx
=[(1/3)x^3 -x +arctanx]|(0->1)
=1/3 -1 +π/4
=π/4 - 2/3
(6)
∫(0->3) |2-x| dx
=∫(0->2) (2-x) dx - ∫(2->3) (2-x) dx
=[2x- (1/2)x^2]|(0->2) - [2x- (1/2)x^2]|(2->3)
=(4-2) +[( 4-2) - (6- 9/2) ]
=2 + ( 2 - 3/2)
=2 + 1/2
=5/2
x^4
=x^2.(1+x^2) -x^2
=x^2.(1+x^2) -(1+x^2) +1
∫(0->1) x^4/(1+x^2)dx
=∫(0->1) [ x^2 -1 + 1/(1+x^2)]dx
=[(1/3)x^3 -x +arctanx]|(0->1)
=1/3 -1 +π/4
=π/4 - 2/3
(6)
∫(0->3) |2-x| dx
=∫(0->2) (2-x) dx - ∫(2->3) (2-x) dx
=[2x- (1/2)x^2]|(0->2) - [2x- (1/2)x^2]|(2->3)
=(4-2) +[( 4-2) - (6- 9/2) ]
=2 + ( 2 - 3/2)
=2 + 1/2
=5/2
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