integrate 2/(5x-1) dx

Question

anonymous · Answer

use substitution method
put 5x- 1 = t

anonymous · Answer

In uv substitution, would that be u?

anonymous · Answer

i think u r asking for integration by parts, here there is not need to apply this rule
put 5x-1 = t
       5dx = dt
         dx = dt/5
therefore (2/5t)*dt
          ( 2/5) ln(t)
put back the value of t in final solution
      (2/5) ln(5x-1)

anonymous · Answer

That makes so much more sense. Thank you! So, if I wanna find whether or not this converges when you take the integral from 1 to infinity, the function diverges, right?

anonymous · Answer

as far as divergence or convergence is concerned, u need to apply leibniz integral rule........and i really dont remember the rule right now.......

anonymous · Answer

We never learned that in class.

anonymous · Answer

sorry that rule was cauchy integral test...........u must have heard of this rule

anonymous · Answer

No

anonymous · Answer

sorry i m not able to recollect

anonymous · Answer

It's okay. Thank you.