Question:
Write a value of $\int \frac{1}{1+e^{x}} d x$.
Solution:
given $\int \frac{1}{1+e^{x}} d x$
$=\int\left(1-\frac{e^{x}}{1+e^{x}}\right) d x$
Let $1+e^{x}=t$
Differentiating on both sides we get,
$E^{x} d x=d t$
Substituting above equation in given equation we get,
$=\int\left(1-\frac{1}{t}\right) d t$
$=t-\log t+c$
$=1+e^{x}-\log \left(1+e^{x}\right)+c$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.