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

Step-by-step Solution

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Solution

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Final Answer

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

Problem to solve:

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

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We can solve the integral $\int2x\left(\cot\left(x\right)^2\right)^2dx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

Learn how to solve logarithmic differentiation problems step by step online.

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

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Learn how to solve logarithmic differentiation problems step by step online. Find the integral int(2xcot(x)^2^2)dx. We can solve the integral \int2x\left(\cot\left(x\right)^2\right)^2dx 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. Now, identify dv and calculate v. Solve the integral.

Final Answer

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

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

Solve integral of 2xdx using basic integralsSolve integral of 2xdx using u-substitutionSolve integral of 2xdx using tabular integration

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0
a
b
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m
n
u
v
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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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Main topic:

Logarithmic Differentiation

Related topics:

Logarithmic DifferentiationAdvanced differentiation

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