Question

How do you integrate `1/(sqrt(25+4x^2))` ?

Answer 1

I would take out, from the square root, `25` getting:

`int1/(5*sqrt(1+4/25x^2))dx=`
`=int1/5*1/(sqrt(1+(2/5x)^2))dx=`
`=1/5*5/2sinh^(-1)(2/5x)+c`
`=1/2sinh^(-1)(2/5x)+c`

Where `sinh^(-1)(x)=`arcsinh(x) is one of the inverse hyperbolic functions .
Have a look at: http://mathworld.wolfram.com/InverseHyperbolicSine.html
for more info.