# Stuck on a calc problem

1. Mar 17, 2005

### andrew410

I need to get the integral for sqrt(25+x^2). I can't seem to get the answer without a arcsinh. Can anyone help me? Thx in advance! :)

2. Mar 17, 2005

### Data

Substitute $$x = 5\tan{\theta}$$.

You may need the identity $$\int \sec{\theta} d\theta = \ln |\sec{\theta} + \tan{\theta}| + C$$ to evaluate the resulting integral.

Last edited: Mar 17, 2005
3. Mar 17, 2005

### HallsofIvy

Generally speaking, seeing "sqrt(25+ x2)" should make you think of
a2+ b2= c2 (the Pythagorean theorem) and then
(a/b)2+ 1= (c/a)2 or "tan2(&theta;)+ 1= csc2(&theta;)"

Factoring a "5" out of the squareroot gives 5 sqrt(1+ (x/5)2) which leads us to think "x/5= tan(&theta;) or Data's x= 5 tan(&theta;).