Integration Questions

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