Integral does not make sense?!

Question

I have a (seemingly) silly question. I wish to calculate the integral: $$ \int x^{d}dx $$ and $$ \int x^{(1-d)}dx. $$ Integrating the first integral, I obtain: $$ \int x^{d}dx=\frac{1}{d+1}x^{d+1}+C $$ Integrating the second integral, I obtain: $$ \int x^{(1-d)}dx.=-\frac{1}{d}x^{-d}+C $$ Both of these integrals should be exactly the same when $d=\frac{1}{2}$. But this does not seem to be the case! What am i doing wrong?

Answer 1

You're going to kick yourself.

$\int x^{(1-d)}dx.=\frac{1}{2-d}x^{2-d}+C$