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Question

ex1ex+1dx=

A
log(ex+e2x1)sec1(ex)+c
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B
log(ex+e2x1)+sec1(ex)+c
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C
log(exe2x1)sec1(ex)+c
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D
log(exe2x1)+c
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Solution

The correct option is A log(ex+e2x1)sec1(ex)+c
ex1e2x1dx.
exe2x1dx1e2x1dx
dexe2x11e2x1dx.1e2x1dx.
logex+e2x11e2x1dx
Let ex=t.
exdx=dt
dx=1tdt
logex+e2x1dttt21
logex+e2x1sec1(t)+c
=logex+e2x1sec1(ex)c.

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