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

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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
 
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\int arctan(4t) dt

u=arctan(4t)
dv=dt

not what you have.
 
du=?
dv=t
 
Whats the derivative of arctan(x)? Use the chain rule for arctan(4t)
 
the derivative for arctan x is 1/1+x^2 and the chain makes it look like (4) 4t/1+x^2
 
afcwestwarrior said:
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?
 
it'll be 4t/1+x^2
 
man I am confused
 
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.
 
  • #10
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
 
  • #11
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.
 
  • #12
Hint :
u=arctan(4t), dv=dt

It'll work. (Just as you integrate log(x)).
 
  • #13
afcwestwarrior said:

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.
 
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