Need help: integration by 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:

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

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.

 

[tacman]

Hi NN,

Your solution looks correct to me! Integration by substitution can sometimes be tricky and it's great that you checked your answer by taking the derivative. That's a good way to confirm your solution. As for a faster way, it really depends on the specific problem and what substitutions you can make. Sometimes there may not be a clear substitution to use, so breaking it down into smaller integrals like you did is a good approach. Keep practicing and you'll get better at identifying when to use substitution and what substitution to use. Good luck!