(vi.)
| ∫∞0 | sin mx | dx = ½ ( | 1 | − | 1 | + | 1 | ), |
| e2πx − 1 | em | m | 2 |
(vii.)
∫π0 log (1 − 2α cos x + α2) dx = 0 or 2π log α according as α < or > 1,
(viii.)
| ∫∞0 | sin x | dx = ½ π, |
| x |
(ix.)
| ∫∞0 | cos ax | dx = ½ πb−1 e−ab, |
| x2 + b2 |
(x.)
| ∫∞0 | cos ax − cos bx | dx = ½ π (b − a), |
| x2 |