1.

Evaluate the following integrals :\(\int\)\(\frac{e^x+1}{e^x+x}\)dx

Answer»

Assume,

ex + x = t 

d(ex + x) = dt 

ex + 1 = dt 

Put t and dt in given equation we get,

⇒ ∫\(\frac{dt}{t}\)

= ln|t| + c. 

But, 

t = ex + x 

= ln| ex + 1| + c



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