Integrating arctan(1/x) with Integration by Parts

In summary, the conversation is about a person seeking help with integrating arctan(1/x) using integration by parts. The conversation includes a suggested approach using u substitution and a discussion about the derivative of ln(x^2 + 1).
  • #1
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im having a bit of trouble, can anyone help me integrate arctan(1/x) using integration by parts?
thanks
 
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  • #2
Here's the first line

[tex] \int \arctan \frac{1}{x} {} dx =x\arctan \frac{1}{x}-\int x \frac{-\frac{1}{x^2}}{1+\frac{1}{x^2}} {} dx [/tex]
 
  • #3
im not really understanding how to get that line. i don't know what to assign as u and dv. the xarctan1/x is the part that confuses me because i don't see where the x comes from
 
  • #4
Take it to be 1* arctan(...) then your dv will be 1.
 
  • #5
that doesn't make any sense to me, but thankyou for trying to help. i don't know what "it" is referring to that I am supposed to be taking as 1*arctan(?)
 
  • #6
ooooh i get it! thank you
 
  • #7
im still getting stuck at xarctan(1/x)-int(-x/x^2+1)
 
  • #8
Can you then integrate

[tex] \int \frac{x}{x^2 +1} {}dx [/tex]

?
 
  • #9
I haven't actually done it but if you are right up to that point then it appears that all you have to do is make a simple u substitution to solve the integral.
[tex] \int \frac{x}{x^2 +1} {}dx [/tex]
 
  • #10
what is the derivative of [tex]\ln(x^2 + 1) [/tex] ?
 

What is the formula for integrating arctan(1/x) with Integration by Parts?

The formula for integrating arctan(1/x) with Integration by Parts is ∫arctan(1/x)dx = xarctan(1/x) - ∫(x/(1+x^2))dx.

What are the steps for integrating arctan(1/x) with Integration by Parts?

The steps for integrating arctan(1/x) with Integration by Parts are as follows:
1. Identify u and dv in the given integral.
2. Use the formula ∫udv = uv - ∫vdu to rewrite the integral.
3. Integrate v and differentiate u.
4. Substitute the values of u, v, and ∫vdu into the formula.
5. Simplify the resulting integral and solve for the final answer.

What is the value of arctan(1/x)?

The value of arctan(1/x) is the angle whose tangent is equal to 1/x. It can also be represented as the inverse tangent of 1/x.

What are the possible substitutions for arctan(1/x)?

Some possible substitutions for arctan(1/x) are:
1. x = tanθ
2. u = 1/x
3. x = 1/tanθ
4. u = arctan(1/x)

How can I check my answer when integrating arctan(1/x) with Integration by Parts?

You can check your answer by differentiating the final result and seeing if it matches the original integrand. You can also use online integration calculators or ask a math tutor for assistance.

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