Question

Integrate the following question.
Integrate 1/1+rootx

Answer 1

Answer:

2[√x -log(1+√x)]

Step-by-step explanation:

let, √x=t

squaring on both sides

x=t^2

differentiating on both sides

dx=2t dt

(integral(1/1+√x)dx)=(integral (2t/1+t))dt

=2(integral (t/1+t)dt)

=2(integral (t+1-1/t+1)dt)

=2(integral (t+1/t+1)dt)-2(integral (1/1+t)dt)

=2(integral (1dt))-2log(1+t)

=2t-2log(1+t)

=2(t-log(1+t))

=2[√x-log(1+√x)]