Solve v/(v-1)^2 Integral: Tips & Tricks

[mundo44]

Cannot figure out the integral of : v/(v-1)^2


I tried partial fractions then integrating but didn't get me anywhere! HELP!

 

[gabbagabbahey]

Partial fractions should work...why not post what you've got?

 

[lkh1986]

Try to solve for A and B: v/(v-1)^2 = A/(v-1) + B/(v-1)^2

 

[elduderino]

simplest solution:

let t=v-1
dt =dv
function now becomes Integrate[(t+1)^2/t dt]

no partial fractions needed

 

[njama]

simplest solution:

let t=v-1
dt =dv
function now becomes Integrate[(t+1)^2/t dt]

no partial fractions needed

If the original integral is:


$$\int{\frac{v}{(v-1)^2}}$$

$$t=v-1 ; v=t+1$$

$$dv=dt$$

$$\int{\frac{t+1}{t^2}$$

Now separate on two fractions and solve two integrals.

 

[elduderino]

yeah.. sorry for tht mistake :P