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integrate (x 2 + x)/(e x +x+1) 2 w.r.t x

integrate  (x2 + x)/(ex+x+1)2 w.r.t x

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Suchita,

 

take ex common from denominator,

 

then you have.............  e-xxe-x(x+1)/(1+xe-x+e-x)2

Make the substitution, 1/(1+xe-x+e-x) = t, and you will get

xe-x/(1+xe-x+e-x)2dx = dt, and xe-x+e-x = (1/t)-1.

So after this substitution, you have Integral of [(1/t)-1] = lnt - t + Const. And substitute for t from above.

 

Hope that helps.

 

All the best,

Regards,

Ashwin (IIT Madras).

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