Question

integrate sinx/1+cosx dx

Answer 1

Log (1/1+cosx) is the anti derivative of this function..
Hope it helps..

Answer 2

Hello!

Your Answer:

It
Problem:


∫sin(x)cos(x)+1dx


Substitute u=cos(x)+1
 
⟶ dx=−1sin(x)du

(Steps):

=−∫1udu

Now solving:

∫1udu

This is a standard integral:

=ln(u)

Plug in solved integrals:

−∫1udu

=−ln(u)

Undo substitution u=cos(x)+1

:

=−ln(cos(x)+1)

The problem is solved:

∫sin(x)cos(x)+1dx

=−ln(cos(x)+1)+C

Hope It Helps.

Have A Nice Day.