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不知道,就是混混,分,也不知道这些个字够不够,我在多发几个试试看
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∫(0->1) xarctanx dx
=(1/2)∫(0->1) arctanx dx^2
=(1/2)[x^2.arctanx]|(0->1)-(1/2)∫(0->1) x^2/(1+x^2) dx
=(1/2)(π/4) - (1/2)∫(0->1) [1- 1/(1+x^2)] dx
=π/8 - (1/2)[ x - arctanx]|(0->1)
=π/8 - (1/2)( 1 - π/4 )
=π/4 - 1/2
=(1/2)∫(0->1) arctanx dx^2
=(1/2)[x^2.arctanx]|(0->1)-(1/2)∫(0->1) x^2/(1+x^2) dx
=(1/2)(π/4) - (1/2)∫(0->1) [1- 1/(1+x^2)] dx
=π/8 - (1/2)[ x - arctanx]|(0->1)
=π/8 - (1/2)( 1 - π/4 )
=π/4 - 1/2
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