Question

Integrate dx/√x+2 + √x+1.

With full step explanation.​

Answer 1

Answer:

The idea is to, of course, do trig-substitution. Since

a2+x2−−−−−−√

suggests that x=atan(θ) would be a good one because the expression simplifies to

asec(θ)

We can also observe that dx will become sec2(θ)dθ. Therefore

∫a2+x2−−−−−−√dx=a2∫sec3(θ)dθ

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