Evaluate the integral after figuring out the proper method to use

[Painguy]

Homework Statement

∫ ((2t+3)^2)/t^2 dt

Homework Equations

The Attempt at a Solution

I figured that I would use integration by parts. The problem I'm having is that we haven't actually learned integration by parts, only the u substitution method. I went ahead and read the book on the proof and several examples, but its still a bit new to me so I'm not sure how to approach he problem.

u=1/t^2
du=-dt/3t^3

∫dv∫=(2t+3)^2 dt
v=(4t^3)/3 +6t^2 +9t

4t/3 +6+9/t - ∫ ((4t^3)/3 +6t^2 +9t)/t^3 dt

Is there a more straight forward way of solving this?

 

[Dick]

Homework Statement

∫ ((2t+3)^2)/t^2 dt

Homework Equations

The Attempt at a Solution

I figured that I would use integration by parts. The problem I'm having is that we haven't actually learned integration by parts, only the u substitution method. I went ahead and read the book on the proof and several examples, but its still a bit new to me so I'm not sure how to approach he problem.

u=1/t^2
du=-dt/3t^3

∫dv∫=(2t+3)^2 dt
v=(4t^3)/3 +6t^2 +9t

4t/3 +6+9/t - ∫ ((4t^3)/3 +6t^2 +9t)/t^3 dt

Is there a more straight forward way of solving this?

Sure there is. Just multiply the numerator out. Then split it up and integrate.

 

[Painguy]

Sure there is. Just multiply the numerator out. Then split it up and integrate.

Oh wow... Thanks for the help. I feel a little silly right now.