Integral help please

Question

mandre · Answer

$$\int\limits\frac{ 1 }{ x ^{\frac{ 1 }{ 5 }}+2 }dx$$

hartnn · Answer

did u try plugging in x = y^5 ?

hartnn · Answer

so that denominator becomes linear

mandre · Answer

I tried everything else lol. That's the one thing I don't like about integrals. Sometimes it takes something simple but you have to be able to spot it.

mandre · Answer

Like a reverse substitution?

hartnn · Answer

reverse ?
what u get after you put x= y^5 ? 
dx = ...?

mandre · Answer

5y^4

hartnn · Answer

so your integral in terms of y is ?

mandre · Answer

I'm really stuck. Sorry

hartnn · Answer

ok, till
5y^4 dy / (y+2)
?

mandre · Answer

Where does the y+2 come from?

hartnn · Answer

whats your denominator before substitution ?
whats your denominator after substitution ?

hartnn · Answer

now where r u stuck? or trying ?

mandre · Answer

The substitution is throwing me for a loop. This doesn't work like u-substitution and that's all I'm used to.

hartnn · Answer

why not try one step at a time
what integral you get after one substitution ?

mandre · Answer

The denominator part is easy. Not sure how you get the numerator.

hartnn · Answer

i asked for the integral....

hartnn · Answer

5y^4 dy / (y+2)
this ?

mandre · Answer

Yes

hartnn · Answer

now do other substitution

y+2 = u 
y = u-2
y^4 = (u-2)^4 = .... ?

dy =... ?

mandre · Answer

Don't worry about it. I'll just hope they don't put a question like that in the exam. Thanks for trying.

hartnn · Answer

we could do it! 
its not difficult...