Integral of (x+1)/(x^2+4x+5)

  • #1
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∫(x+1)/(x^2 + 4x +5) dx
Anyone can help me doing it using Arctan and ln
 

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  • #2
blue_leaf77
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Let's first hear out your own idea to solve this problem? What strategy you have in mind?
 
  • #3
Let's first hear out your own idea to solve this problem? What strategy you have in mind?
∫(x+1)/(x^2+4x+5) dx = 1/2∫ (2x+2)/(x^2+4x+5) dx = 1/2∫(2x+4)/(x^2+4x+5) dx + 1/2∫(-2)/(1+(x+2)^2) dx
[1/2 ln l(x^2+4x+5)l ] - arctan(x+2)
SO??
 
  • #4
HallsofIvy
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Don't forget the "constant of integration".
 
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  • #6
phion
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Try re-writing the original expression into something more manageable.
 

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