Question

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

Answer 1

how did this become:

Answer 2

@hartnn

Answer 3

@amistre64

Answer 4

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

Answer 5

uhmm as long as we get the solution..

Answer 6

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

Answer 7

yes i did attached a file right?

Answer 8

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 ??

Answer 9

x=a sin theta?

Answer 10

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

Answer 11

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

Answer 12

@hartnn ?

Answer 13

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))

Answer 14

now wats next?