Integrate this: Integration of (tan inverse x)^2 using integration by parts

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In summary, there is a function f(x) that involves the integration of (tan inverse x)^2. One approach to solving it is by using the product rule and substitution. Another approach is to use the formula for the derivative of arctan x. Good luck!
  • #1
sunip
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integrate this...

integration of (tan inverse x)^2
 
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  • #2
Please show any work you have done or thoughts you have had before we start helping.
 
  • #3
did your function meen

f(x)=(arctan x)^2

if its true
then
make
f(x)=(arctan x)(arctan x)
and solve it by parts
remmember that
the derivative of arctan x is 1/(1+x^2)
then i think you should take a subtitution of arctan x=t
because you would have arctan x and its derivative in the same integral

i am not sure its the right way

another way to do by parts is to take 1 as u'
and the rest of the function to take as V
just some thoughts
good luck
 
Last edited:

What is integration?

Integration is a mathematical process that involves finding the area under a curve. It is used to solve problems in various fields such as physics, engineering, and economics.

Why is integration important?

Integration is important because it allows us to calculate quantities that are difficult or impossible to measure directly. It is also used to model real-world situations and make predictions.

What are the different methods of integration?

The main methods of integration are the fundamental theorem of calculus, substitution, integration by parts, partial fractions, and trigonometric substitution. These methods are used to solve different types of integrals.

How do you integrate a function?

To integrate a function, you need to follow a set of rules and techniques depending on the type of integral. These include finding the antiderivative, using substitution to simplify the integral, and applying integration by parts or other methods if necessary.

What are some applications of integration?

Integration has many applications in various fields such as physics, engineering, economics, and statistics. Some examples include calculating the area under a velocity-time graph to find the displacement of an object, finding the volume of irregular shapes, and calculating the expected value in probability and statistics.

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