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# Find the integral $\int2x\left(\cot\left(x\right)^2\right)^2dx$

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asin
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##  Final answer to the problem

$-\frac{2}{3}x\cot\left(x\right)^{3}+x^2+2x\cot\left(x\right)-\frac{1}{3}\cot\left(x\right)^{2}-\frac{8}{3}\ln\left|\sin\left(x\right)\right|+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

• Integrate using basic integrals
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Product of Binomials with Common Term
• FOIL Method
Can't find a method? Tell us so we can add it.
1

Simplify $\left(\cot\left(x\right)^2\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $2$

$\int2x\cot\left(x\right)^{4}dx$

Learn how to solve differential equations problems step by step online.

$\int2x\cot\left(x\right)^{4}dx$

Learn how to solve differential equations problems step by step online. Find the integral int(2xcot(x)^2^2)dx. Simplify \left(\cot\left(x\right)^2\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 2. The integral of a function times a constant (2) is equal to the constant times the integral of the function. We can solve the integral \int x\cot\left(x\right)^{4}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du.

##  Final answer to the problem

$-\frac{2}{3}x\cot\left(x\right)^{3}+x^2+2x\cot\left(x\right)-\frac{1}{3}\cot\left(x\right)^{2}-\frac{8}{3}\ln\left|\sin\left(x\right)\right|+C_0$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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0
a
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m
n
u
v
w
x
y
z
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(◻)
+
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×
◻/◻
/
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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

###  Main Topic: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.