How do you integrate #int_0^1 1/(1+(x)^(1/2)) dx# ?
2 Answers
Write
To do the indefinite integral, I used a tip from WolframAlpha :
Let
We need to solve for
But
Perform the substitutions:
Add 0 to the numerator in the form if
Separate into two fractions:
The first fraction becomes 1:
Both terms are trival to integrate:
Reverse the substitution:
To integrate from 0 to 1 we evaluate the right side at
The constants of integration sum to 0 and
let
differentiating both the sides,
applying simple polynomial division,
replacing,
now, applying the limits,