∫x/(x^4+2(x^2)+5)dx
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∫x/(x^4+2(x^2)+5)dx
∫x/(x^4+2(x^2)+5)dx
∫x/(x^4+2(x^2)+5)dx
令a=x²
原式=1/2*∫dx²/(x^4+2x²+5)
=1/2*∫da/(a²+2a+1+4)
=1/2*∫da/[(a+1)²+4]
=1/8*∫da/[(1/4)(a+1)²+1]
=1/8*∫da/[(a/2+1/2)²+1]
=1/4*∫d(a/2+1/2)/[(a/2+1/2)²+1]
=1/4*arctan((a/2+1/2)+C
=1/4*arctan(x²/2+1/2)+C
①(y+1)÷4=(x+2)÷3
两边乘以12
3(y+1)=4(x+2)
3y+3=4x+8
3y=4x+5
代入②2x-3y=1
2x-(4x+5)=1
2x-4x-5=1
2x=-6
x=-3
所以3y=4x+5=-7
所以x=-3,y=-7/3
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