33.7. EXERCISES 685
Integrate by parts in the inside integral to obtain
=∫
∞
0
1t2 +1
− e−rt(
cosr1+ t2 + t
sinr1+ t2
)dt
=π
2−∫
1√1+ t2
e−rt cos(r−φ (t))dt
Explain why the second integral converges to 0 as r → ∞.
