i iπ ax
Z
sech(ax) dx = log tanh +
a 4 2
Z
1
coth(ax) dx = log sinh(ax)
a
Z
1 x
x sin ax dx = sin ax − cos ax
a 2 a
2 2
Z 2x a x − 2
2
x sin ax dx = sin ax − cos ax
a 2 a 3
Z
1 x
x cos ax dx = cos ax + sin ax
a 2 a
2 2
Z 2x cos ax a x − 2
2
x cos ax dx = + sin ax
a 2 a 3
90