Thread: another integration with substitution of trig/hyperbolic function

1. another integration with substitution of trig/hyperbolic function

i dont know wat to substitute for this integral
$
\int \sqrt{1 + 4x^2} dx
$

pls help me

2. i tried substituting

$
x = 1/2 tan t
$

but that was no good..unless i was wrong...

3. Originally Posted by tasukete
i tried substituting

$
x = 1/2 tan t
$

but that was no good..unless i was wrong...
It works but you have to be able to integrate sec^3 t ..... This might be difficult for you.

A better (easier) substitution would be x = 1/2 sinh t ..... Are you familiar with hyperbolic functions?

4. Originally Posted by mr fantastic
It works but you have to be able to integrate sec^3 t ..... This might be difficult for you.

A better (easier) substitution would be x = 1/2 sinh t ..... Are you familiar with hyperbolic functions?
yes thank you . I managed to solve it using x = 1/2 sinh t.
The book that im using is pretty old... so it doesn't show hyperbolic subsitutions..it only gives me trig substitutions for these problems.

I've come to realise that hyperbolic substitutions are much faster and easier in these situations...