# What is #int arctan(x^2) dx#?

Here,

So,

#=1/sqrt2tan^-1((x-1/x)/sqrt2)+1/(2sqrt2)ln|(x+1/x- sqrt2)/(x+1/x+sqrt2)|+c#

#I_A=1/sqrt2tan^-1((x^2-1)/(sqrt2x))+1/(2sqrt2)ln|(x^2- sqrt2x+1)/(x^2+sqrt2x+1)|+c#

#I=xtan^-1x^2-1/sqrt2tan^-1((x^2-1)/(sqrt2x))-1/(2sqrt2)ln|(x^2- sqrt2x+1)/(x^2+sqrt2x+1)|+c#

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The integral of arctan(x^2) with respect to x is not expressible in terms of elementary functions. It cannot be represented by a combination of polynomials, exponential functions, logarithmic functions, trigonometric functions, or their inverses. Therefore, it is considered a non-elementary integral.

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The integral of ( \arctan(x^2) ) with respect to ( x ) is not expressible in terms of elementary functions. It cannot be represented by a combination of polynomials, exponentials, logarithms, trigonometric functions, or their inverses. Therefore, the integral ( \int \arctan(x^2) , dx ) does not have a simple analytical solution.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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