Mathematics Formula Sheet Page 6
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Integration (+ constant;
a
0
where relevant)
Function
Integral
tan
x
ln
sec
x
cot
x
ln
sin
x
−
+
=
1
cosec
x
ln
cosec
x
cot
x
ln
tan(
x
)
2
π
+
=
1
+
1
sec
x
ln
sec
x
tan
x
ln
tan(
x
)
2
4
2
sec
x
tan x
sinh
x
cosh
x
cosh
x
sinh
x
tanh
x
ln
cosh
x
⎛
⎞
1
x
−
1
<
⎜
⎟
sin
(
x
a
)
⎝
a
⎠
2
2
a −
x
⎛
⎞
1
1
x
−
1
tan
⎜
⎟
2
2
a +
a
⎝
a
⎠
x
⎛
⎞
1
x
{
}
−
1
2
2
=
+
−
>
⎜
⎟
cosh
ln
x
x
a
(
x
a
)
⎝
a
⎠
2
2
x −
a
⎛
⎞
1
x
{
}
−
1
2
2
=
+
+
⎜
⎟
sinh
ln
x
x
a
⎝
a
⎠
2
2
a +
x
+
⎛
⎞
1
1
a
x
1
x
−
1
=
<
⎜
⎟
ln
tanh
(
x
a
)
−
2
2
2
a
a
x
a
a
a −
⎝
⎠
x
−
1
1
x
a
ln
+
2
2
x −
2
a
x
a
a
∫
d
v
∫
d
u
=
−
u
d
x
uv
v
d
x
d
x
d
x
6
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