Evaluate the integral. ∫x5x−1dx



Answered question


Evaluate the integral. x5x1dx

Answer & Explanation



Skilled2020-10-21Added 119 answers

The key in this situation is to adjust the variables. In particular, if you encounter a square root, you should either set it to something squared under the square root or convert it to something else u= whichever is beneath it. We'll choose the latter in this instance.
Let u=5x1.Then, because we know du=du dx  dx , we see that du=5dx which is equivalent to k dx =1du. We obtain by substituting these into the integral.
This is a portion of what we want, but there is still a xx in there, and we like to completely switch to uu's. I mean, keep in mind that we set u=5x1. Let's solve that for x in terms of u:
By replacing this, we obtain

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