How do you integrate $(1/(25 + x^2) ) dx$ ?

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Answer 1 · 2015-05-18T00:11:05

We can rewrite this as

$int(1/(5^2+x^2))dx$

By definition, we know that the integration of the inverse of a sum of squares results in a trigonometric function as follows:

$int(1/(u^2+a^2))du=(1/a)arctan(u/a)+c$

Applying this formula to your function, we have this:

$int(1/(5^2+x^2))dx=color(green)((arctan(x/5))/5+c)$

How do you integrate (1/(25 + x^2) ) dx(1/(25 + x^2) ) dx?