Help with Integral question?

Question

How would I do this Integral?

&#8747 (3)/(1+x^2) dx

Answer 1

Let x=tan(u) ------ means u = aractan(x)

dx=sec^2(u) du

The given integral becomes

∫ 3 sec^2(u) du / ( 1+tan^2(u))

Since 1+tan^2(u) = sec^2(u)

The integral becomes

∫ 3 du

=3u +C

=3 arctan(x) + C

Answer 2

its simple..integral 1/(1+x^2) is tan inverse x..so the ans is 3 X tan inv(x)

Answer 3

I also don't know how to make integral symbol, sorry, but I think I can solve the problem, so I will symbolize it as "f".

First suppose x = tan a

we will get that dx=sec^2 a da

f (3/(1+tan^2 a))*sec^2 a da

We know that 1 + tan^2 x= sec^2 x.So

=f(3 sec^2 a/ sec^2 a) da

=f 3 da

=3a +c

we know that x = tan a

so a = arc tan x

so the result of the integral is  3arctan x +c