Trig Substitution

[uberathlete]

Hi everyone. I'm really having problems figuring out how to get this integral with trig substitution:

intgral sign 1 / (2x^2+1) dx .

I know how to get the integral if the denominator didn't have a 2 attached to the x^2, but I'm having problems with the one above. Can someone please show me step by step, how the integral is found? This isn't a homework problem or anything, so I just want to understand the whole process. Thanks!

 

[robbwrr]

if it were int{dx /( u^2 + 1) } you'd have arctan{u}

so let 2x^2 = u^2 or u= xsqrt{2} and it becomes:

int{ (1/sqrt{2}) {du / (u^2+1)} = (1/sqrt{2}) arctan{u}=(1/sqrt{2}) arctan{xsqrt{2}}

 

[uberathlete]

if it were int{dx /( u^2 + 1) } you'd have arctan{u}

so let 2x^2 = u^2 or u= xsqrt{2} and it becomes:

int{ (1/sqrt{2}) {du / (u^2+1)} = (1/sqrt{2}) arctan{u}=(1/sqrt{2}) arctan{xsqrt{2}}

Holy cow :shock: ! Now I get it. Thanks robbwrr.