令t=2x+1,x=(t-1)/2 dx=dt/2
∫xdx/(4x^2+4x+5)
=∫(t-1)/2 *dt/2 /(t^2+4)
=1/8*∫(2t-2)/(t^2+4) *dt
=1/8 *∫1/(t^2+4)*d(t^2+4)-1/4*∫dt/(t^2+4)
=1/8*ln(t^2+4)-1/8*∫d(t/2)/((t/2)^2+1)
=1/8*ln(t^2+4)-1/8arctg(t/2)+c
1/8ln(4x^2+4x+5)-1/8arctg(x+1/2)+c
令t=2x+1,x=(t-1)/2 dx=dt/2
∫xdx/(4x^2+4x+5)
=∫(t-1)/2 *dt/2 /(t^2+4)
=1/8*∫(2t-2)/(t^2+4) *dt
=1/8 *∫1/(t^2+4)*d(t^2+4)-1/4*∫dt/(t^2+4)
=1/8*ln(t^2+4)-1/8*∫d(t/2)/((t/2)^2+1)
=1/8*ln(t^2+4)-1/8arctg(t/2)+c
1/8ln(4x^2+4x+5)-1/8arctg(x+1/2)+c