Integration using Hyperbolic

**BabyMilo** · February 16th 2011, 10:30 AM

$\int \frac{x}{\sqrt{x^2+4x}} dx<br />$
use substitution $x+2=2cosh\theta$

$\int \frac{x}{\sqrt{(x+2)^2-4}} dx$

$\int \frac{x}{\sqrt{(2cosh\theta)^2-4}} dx$

$\int \frac{x}{\sqrt{(4cosh^2\theta)-4}} dx$

$\int \frac{x}{2\sqrt{(cosh^2\theta)-1}} dx$

$\int \frac{(2cosh\theta-2)2sinh\theta}{2sinh\theta} d\theta$

$\int 2cosh\theta-2 d\theta$

$= 2sinh\theta -2\theta + C$

but it doesnt seem right.

where did i go wrong?

thanks.

**zzzoak** · February 16th 2011, 12:34 PM

Seems good to me. But is difficult to get $\theta =f(x)$ .
May be more simple is

$<br /> \int \frac{(x+2)-2}{\sqrt{(x+2)^2-4}} dx=\int \frac{x+2}{\sqrt{(x+2)^2-4}} dx-\int \frac{2}{\sqrt{(x+2)^2-4}} dx<br />$

**BabyMilo** · February 16th 2011, 12:45 PM

Looks wrong to me.
http://www.wolframalpha.com/input/?i=intg+%28x%29%2F%28x^2%2B4x%29^0.5+0+to+1
$\int \frac{x}{\sqrt{x^2+4x}} dx$
this gives 0.311

$\int 2cosh\theta-2 d\theta$
this gives 0.350

someone help?

thanks

**zzzoak** · February 16th 2011, 01:36 PM

Please look here
integrate (2*cosh x -2)dx from x=0 to 0.96242 - Wolfram|Alpha

Thread: Integration using Hyperbolic

LinkBack

Thread Tools

Display

Integration using Hyperbolic

Similar Math Help Forum Discussions

Integration Using Hyperbolic Identities

Integration with Hyperbolic Sine

Integration? Hyperbolic?

Integration using the hyperbolic functions

hyperbolic integration

Search Tags