Is This the Correct Way to Integrate arctan(4t) by Parts?

[afcwestwarrior]

Homework Statement

∫arctan 4t dt

Homework Equations

integration by parts
∫u dv= uv- ∫v du


3. The attempt at a
u=arctan dv=4tdt
du=1/x^2+1 v=t/2

are these correct, the arctan throws me off

 

[rock.freak667]

$$\int arctan(4t) dt$$

u=arctan(4t)
dv=dt

not what you have.

 

[afcwestwarrior]

du=?
dv=t

 

[Feldoh]

Whats the derivative of arctan(x)? Use the chain rule for arctan(4t)

 

[afcwestwarrior]

the derivative for arctan x is 1/1+x^2 and the chain makes it look like (4) 4t/1+x^2

 

[rock.freak667]

the derivative for arctan x is 1/1+x^2 and the chain makes it look like (4) 4t/1+x^2

if x=4t

$$\frac{d}{dx}(arctan(x))=\frac{1}{1+x^2}$$

so get the differential of arctan(4t), you'll need to multiply $\frac{d}{dx}(arctan(x))$ by $\frac{dx}{dt}$. What does this give you?

 

[afcwestwarrior]

it'll be 4t/1+x^2

 

[afcwestwarrior]

man I am confused

 

[Defennder]

You're working in t, not x. As said earlier, use the chain rule for this. Let u=4t. d/dt arctan (4t) = du/dt d/du arctan(u). Express everything in t when you're done.

 

[rock.freak667]

Let y=arctan(4t).

Let u=4t.

So we have y=arctan(u). What is dy/du?What is du/dt?

EDIT: ahh Defennder, you type fast

 

[Gib Z]

I'm pretty damn confused here as well. Half these posts are showing him how to find the derivative when he wants to know the antiderivative lol. I mean sure, its probably more important to know the derivative first, but that's not what he asked for.

 

[weejee]

Hint :
u=arctan(4t), dv=dt

It'll work. (Just as you integrate log(x)).

 

[HallsofIvy]

Homework Statement

∫arctan 4t dt

Homework Equations

integration by parts
∫u dv= uv- ∫v du


3. The attempt at a
u=arctan dv=4tdt
du=1/x^2+1 v=t/2

are these correct, the arctan throws me off

Surely you understand that "arctan 4t" does NOT mean "arctan" time "4t"! "arctan" without a variable is meaningless.