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Solve the trigonometric integral $\int\arctan\left(x\right)dx$

Used Formulas

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asin
acos
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acot
asec
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sinh
cosh
tanh
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asinh
acosh
atanh
acoth
asech
acsch

Solution

Formulas

Videos

Trigonometric Integrals

$\int\tan\left(\theta \right)dx=-\ln\left(\cos\left(\theta \right)\right)+C$

Function Plot

Plotting: $x\arctan\left(x\right)-\frac{1}{2}\ln\left(1+x^2\right)+C_0$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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$\int\arccsc\left(x\right)dx$

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$\int arctan\:x\:dx$

Main Topic: Integration by Trigonometric Substitution

Trigonometric substitution is the substitution of trigonometric functions for other expressions. One may use the trigonometric identities to simplify certain integrals containing radical expressions.

Used Formulas

See formulas (1)

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