I'm trying to integrate sqrt. x^2 + 4x +5 (Integrals involving quadratics) and i'm stuck with int. sec^3 theta d(theta) .. pls. someone help me

Question

anonymous · Answer

how did this become:

anonymous · Answer

@hartnn

anonymous · Answer

@amistre64

hartnn · Answer

i think we did, sec^3 theta
and you want same & exact that answer or any form will do ?

anonymous · Answer

uhmm as long as we get the solution..

hartnn · Answer

so, where u stuck ? we did sec^3 theta right ?

anonymous · Answer

yes i did attached a file right?

hartnn · Answer

your original Q is  sqrt. x^2 + 4x +5 , right ? 
so instead of trigo. substitution, can you use standard formula for 
 sqrt. x^2+ a^2 ??

anonymous · Answer

x=a sin theta?

hartnn · Answer

$ \sqrt {x^2 + 4x +5}=\sqrt{(x+2)^2+1}$
after u put u = x+2, du=dx,you get a standard integral $\int \sqrt{u^2+1}du$

anonymous · Answer

ok..how to integrate sqrt of u^2 +1?

anonymous · Answer

@hartnn ?

amistre64 · Answer

sec^3

sec sec^2

sec (tan^2 + 1)

sec tan tan  + sec

integratation should be pretty straight forward, except for that sec, which has the trick of (sec+tan)/(sec+tan))

anonymous · Answer

|dw:1360142698514:dw|
now wats next?