`int1/(25+4x^2)dx`
Let's transform the denominator of the integral,
`int1/(25+4x^2)dx=int1/(4(x^2+25/4))dx`
Take the constant out,
`=1/4int1/(x^2+(5/2)^2)dx`
Now use the standard integral:`int1/(x^2+a^2)dx=1/aarctan(x/a)`
`=1/4(1/(5/2))arctan(x/(5/2))`
simplify and add a constant C to the solution,
`=(1/4)(2/5)arctan((2x)/5)+C`
`=1/10arctan((2x)/5)+C`
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