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

Used Formulas

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Solution

Formulas

Videos

Basic Integrals

· Constant factor Rule
$\int cxdx=c\int xdx$
· Sum Rule for Integration
$\int\left(a+b+...\right)dx=\int adx+\int bdx+...$
· Power Rule of Integration
$\int xdx=\frac{1}{2}x^2+C$

Basic Derivatives

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

Trigonometric Integrals

$\int\cot\left(\theta \right)^ndx=\frac{-1}{n-1}\cot\left(\theta \right)^{\left(n-1\right)}-\int\cot\left(\theta \right)^{\left(n-2\right)}dx$
$\int\cot\left(\theta \right)^2dx=-\theta -\cot\left(\theta \right)+C$
$\int\cot\left(\theta \right)dx=\ln\left(\sin\left(\theta \right)\right)+C$

Integration Techniques

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

Function Plot

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

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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

How to improve your answer:

Similar Problems Solved

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Compute the integral

$\int\left(\frac{x}{2}+3\right)^2dx$

Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

Used Formulas

8. See formulas

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