Evaluate the integral. int x sqrt(5x-1) dx

sjeikdom0

sjeikdom0

Answered question

2020-10-20

Evaluate the integral. x5x1dx

Answer & Explanation

unett

unett

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.
xu15du
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:
5x=u+1x=u+15
By replacing this, we obtain
u+15u15du=125(u+1)udu=125(u32+u12)du

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