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Z
1 √
2
2
√ dx = log(x + x ± a )
2
x ± a 2
Z
1 1 −1 x
√ dx = sec
2
x x − a 2 |a| a
√
Z 2 2
1 1 a + a ± x
√ dx = − log
2
x a ± x 2 a x
Z
1
sin(ax) dx = − cos(ax)
a
Z
1
cos(ax) dx = sin(ax)
a
Z
1
tan(ax) dx = − log cos(ax)
a
Z
1 ax
csc(ax) dx = log tan
a 2
Z
1 π ax
sec(ax) dx = log tan +
a 4 2
Z
1
cot(ax) dx = log sin(ax)
a

Z
1
sinh(ax) dx = cosh(ax)
a
Z
1
cosh(ax) dx = sinh(ax)
a
Z
1
tanh(ax) dx = log cosh(ax)
a
Z
1 ax
csch(ax) dx = log tanh
a 2
Z
i iπ ax
sech(ax) dx = log tanh +
a 4 2

Z
1
coth(ax) dx = log sinh(ax)
a

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