Question

where is (cosx - cos2x)/sinx divergent?

Answer 1

I feel the questions lacks some content.

Answer 2

Z 5
2
dx
√
3x − 6
= 6 (convergent) (1)
Z ∞
0
dx
x
2 + 4
=
π
4
(convergent) (2)
Z 1
0
ln(x) dx = −1 (convergent) (3)
Z ∞
0
e
x
e
2x + 1
dx =
π
4
(convergent, u = e
x
) (4)
Z ∞
−∞
x
x
4 + 1
dx = 0 (convergent) (5)
Z ∞
0
xex
dx (divergent)