How does one integrate this?
Integrate [ 1 / (1 + x^(1/2)) ]
Ans: -2 ln |x^(1/2) + 1| + 2 x^(1/2)
Thanks.
Hi,
Consider applying the substitution u = sqrt(x). Thanks!
Cheers,
Wen Shih
P.S. In H2 maths, the substitution will be given.
Yah hor.
I tried substituting u = 1 + sqrt (x), didn't think of u = sqrt (x).
Hmmm......
du/dx = 1/2 (x)^(-1/2)
But the numerator doesn't have a corresponding dx = du / 1/2 (x)^(-1/2) to turn it into a natural log.
Hi,
Let u = sqrt(x). Then du/dx = 1 / {2 sqrt(x)} = 1 / (2u).
Now integral [ 1 / {1 + sqrt(x)} ] dx = integral [ 1 / (1 + u) ] (2u) du.
= 2 integral [ 1 - 1/(u + 1) ] du.
I believe you should be able to continue from this point on. Thanks!
Cheers,
Wen Shih
Originally posted by wee_ws:Hi,
Let u = sqrt(x). Then du/dx = 1 / {2 sqrt(x)} = 1 / (2u).
Now integral [ 1 / {1 + sqrt(x)} ] dx = integral [ 1 / (1 + u) ] (2u) du.
= 2 integral [ 1 - 1/(u + 1) ] du.
I believe you should be able to continue from this point on. Thanks!
Cheers,
Wen Shih
It's a lot clearer now.
Thanks.