# What is the antiderivative of #2/(x^2+1)#?

Normally this may be quoted as a standard integral:

However to convince yourself this is indeed the case:

First consider the trig - identity:

Now going back to the integral, use the substitution:

This will also mean:

Now using the trig-identity we just saw we can replace the denominator giving us:

Now reverse the substitution and we get:

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The antiderivative of ( \frac{2}{x^2 + 1} ) is ( 2 \arctan(x) + C ), where ( C ) is the constant of integration.

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