Integrals with Trig Sustitution:?

Question

When we have sqrt(a^2 - x^2)

we say that adj = sqrt(a^2 - x^2) right?

so, what do we use with

sqrt(a^2+x^2)
and with sqrt(x^2-a^2) ???

Answer 1

sqrt(x^2+a^2) --> let z=x/a then a*sqrt(z^2+1) then let z=tan(q) so tan^2(q)+1 = sec^2(q)

then a*sqrt(z^2+1) = a*sec(q)