Solve the trigonometric integral $\int\csc\left(x\right)^3dx$

Used Formulas

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e
π
ln
log
log
lim
d/dx
Dx
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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

Derivatives of trigonometric functions

· Derivative of cosecant function
$\frac{d}{dx}\left(\csc\left(\theta \right)\right)=-\frac{d}{dx}\left(\theta \right)\csc\left(\theta \right)\cot\left(\theta \right)$

Basic Derivatives

· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$

Trigonometric Integrals

$\int\csc\left(\theta \right)^2dx=-\cot\left(\theta \right)+C$
$\int\csc\left(\theta \right)dx=-\ln\left(\csc\left(\theta \right)+\cot\left(\theta \right)\right)+C$

Integration Techniques

· Integration by Parts
$\int udv=uv - \int vdu$

Basic Integrals

· Constant factor Rule
$\int cxdx=c\int xdx$
· Sum Rule for Integration
$\int\left(a+b+...\right)dx=\int adx+\int bdx+...$

Function Plot

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

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1
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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
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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