# Integral of irrational function

### Integral of irrational function

Integral of an irrational function:
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### Re: Integral of irrational function

a is a positive real number.
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### Re: Integral of irrational function

Both solutions are correct, because
$$\arcsin(x/a) = \arctan(x/\sqrt{a^2-x^2})$$.

You can prove this by considering a right angled triangle with hypotenuse $$a$$, opposite side $$x$$, and by Pythagoras the adjacent side is $$\sqrt{a^2-x^2}$$. So $$\sin\theta = x/a$$, and $$\tan\theta = x/\sqrt{a^2-x^2}$$, which means we have two ways of calculating $$\theta$$ which results in $$\theta = \arcsin(x/a) = \arctan(x/\sqrt{a^2-x^2})$$.

https://en.wikipedia.org/wiki/Inverse_t ... _functions

Hope this helped,

R. Baber.
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