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  • Integrate: ( 2x +1 ) / ( x^2 +4x +1 ) ^3/2

Integrate: ( 2x +1 ) / ( x^2 +4x +1 ) ^3/2

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Solution:

                   I=int frac2x+1(x^2+4x+1)^frac32dx=int frac2x+1x^3(1+frac4x+frac1x^2)dx

          \ \ Rightarrow I= int frac2x^-2+x^-3(1+frac4x+frac1x^2)^frac32dx 

          Put      frac1x^2+frac4x+1=t^2Rightarrow -frac2x^3-frac4x^2dx=2t dt

      Rightarrow         I=fracx(x^2+4x+1)^frac12+c

Posted by

Deependra Verma

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