how does one integrate: 1/(x + x^(4/5)) ? It's been a while, Iam trying to help someone study for a test.

Answer 1

∫1/(x+x^(4/5)) dx

Let u=x^(1/5). Then du=1/5 x^(-4/5) dx, and dx = 5 u^4 du. So this becomes:

∫5 u^4/(u^5 + u^4) du

Canceling:

∫5/(u+1) du

Which integrates easily as:

5 ln |u+1| + C

Resubstituting, we have:

5 ln |x^(1/5) + 1| + C

And we are done.

Edit: Oops! I forgot the constant 5 the first time around. Sorry about that. The integral is correct now.

Answer 2

its been awhile for me too, but i have an idea that might work. factor the denominator and use partial fraction decomposition to break in down and then integrate the pieces. (if you try it let me know if it works out)