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What is the Integration of 1/(1+atan(x))dx please provide the solution of above problem

  • What is the Integration of 1/(1+atan(x))dx
  • please provide the solution of above problem

  •  

Grade:12th pass

1 Answers

Aditya Gupta
2080 Points
2 years ago
put tanx=y
we get dy=(1+y^2)dx
or dy/[(1+y^2)(1+ay)]
now simply write in form of partial fractions:
1/[(1+y^2)(1+ay)]= c/(1+ay) + (fy+e)/(1+y^2) and determine the coefficients c d and f
c/(1+ay) is integrated as cln(1+ay)/a
write (fy+e)/(1+y^2) as (fy)/(1+y^2) + (e)/(1+y^2)
 (e)/(1+y^2) has integral e*arctany.
(fy)/(1+y^2) can be solved by letting 1+y^2=z so its integral is
f/2*ln(1+y^2)
add all these together now and thats it

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