求下列广义积分！ 20
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(2)
∫[1：+∞]dx/[x(x+1)]
=ln|x/(x+1)||[1：+∞]
=ln1 -ln|1/(1+1)|
=0-ln½
=ln2
(4)
∫[-∞：+∞]dx/(x²+2x+2)
=∫[-∞：+∞]d(x+1)/[1+(x+1)²]
=arctan(x+1)|[-∞：+∞]
=π/2 -(-π/2)
=π
∫[1：+∞]dx/[x(x+1)]
=ln|x/(x+1)||[1：+∞]
=ln1 -ln|1/(1+1)|
=0-ln½
=ln2
(4)
∫[-∞：+∞]dx/(x²+2x+2)
=∫[-∞：+∞]d(x+1)/[1+(x+1)²]
=arctan(x+1)|[-∞：+∞]
=π/2 -(-π/2)
=π
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