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

## Step-by-step Solution

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### Videos

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

Problem to solve:

$\int2x\cdot\cot\left(^2\right) x^2dx$

Specify the solving method

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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 integration by parts problems step by step online.

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

Learn how to solve integration by parts 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 u and calculate du.

$2x\left(-\frac{1}{3}\cot\left(x\right)^{3}+x+\cot\left(x\right)\right)-\frac{8}{3}\ln\left(\sin\left(x\right)\right)-\frac{1}{3}\cot\left(x\right)^{2}-x^2+C_0$
SnapXam A2

### beta Got another answer? Verify it!

Go!
1
2
3
4
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

$\int2x\cdot\cot\left(^2\right) x^2dx$

### Main topic:

Integration by Parts

~ 0.17 s