Question

Why does integral 1/(x^2+4) = 1/2 arctan (x/2) + C ?

Answer 1

Why does\[\int\limits_{}^{}\frac{ 1 }{ x ^{2} + 4 } = \frac{ 1 }{ 2 }\arctan(\frac{ x }{ 2 })+C\]

Answer 2

I know that \[\int\limits_{}^{}\frac{ 1 }{x ^{2} +1 } = \arctan(x)\] But I cant seem to figure out why the above is true

Answer 3

Magic, what else? ^.^

Answer 4

pfff
\[\Large \int \frac{1}{x^2+4}dx=\int \frac{1}{4\left(\frac{x^2}{4}+1\right)}dx=\frac14\int \frac{1}{\frac{x^2}{4}+1}dx\]