What is 1x25?

When I use an online integral calculator, it's suggesting I use substitution and let u=x5

I don't understand how to get the 5. Is there an alternative way of solving this?
If not - what does the 5 mean and how do I work this out for similar questions?

2 Answers
May 16, 2017

lnx5x+525+C

Explanation:

1x25=15(15)(x25)=151x251=151(x5)21

Now if we set u=x5 then the numerator must be 15 since dudx[u]=15 to apply the substitition rule.

15(15)(15)1(x5)21dx

It is now all set for substitution:
551u21du=(55)[12(1u1du1u+1du)]=(125[ln(u1)ln(u+1)])=ln[u1u+1]25

Undo substitution:
ln[x51x5+1]25=lnx5x+525+C

Absolute value for the domain.

I use to solve this way:
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