# How to solve#intarctan(sqrt(x))dx#?

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#### Explanation

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It is difficult to work with the

Let

#=int2tarctan(t)dt#

Next, we will apply integration by parts. To apply the formula

Applying the formula, this gives

Focusing on the remaining integral, we have

#=intdt - int1/(1+t^2)dt#

#=t - arctan(t) + C#

Putting this all together, we get our final result:

#= t^2arctan(t)-intt^2/(1+t^2)dt#

#=t^2arctan(t) - t+arctan(t) + C#

#=(t^2+1)arctan(t) - t + C#

#=(x+1)arctan(sqrt(x))-sqrt(x)+C#

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