Integration of (t+1)²/t² without substitution

[maxpayne_lhp]

Hello all, how are you?

we are currently working on integration by substitution, what do you guys think about the way i solved this one:

Find: $$\int \frac{(t+1)^2}{t^2} dt$$

My solution:

$$\int \frac{(t+1)^2}{t^2} dt<br /> <br /> = \int 1dt + \int \frac{2}{t} dt + \int \frac{1}{t^2} dt<br /> <br /> = t + 2ln|t| + \frac{1}{-3t^3}<br />$$

When i check it by takin the derivative of my answer... it matches up with the stuff up top... but there's no substitution... am i doing it the right way? is there any faster way?

Thanks,

NN

Note:I realized i posted this at a wrong section... please move it if you can. Thanks and sorry about that.

 

[arunbg]

Don't forget the constant of integration! I don't think there is a quicker way of solving it.