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

Step-by-step Solution

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Final Answer

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

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Expand the integral $\int\left(2x\cot\left(x\right)^2+x^2\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

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

Learn how to solve integrals of rational functions problems step by step online.

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

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Learn how to solve integrals of rational functions problems step by step online. Find the integral int(2xcot(x)^2+x^2)dx. Expand the integral \int\left(2x\cot\left(x\right)^2+x^2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int2x\cot\left(x\right)^2dx results in: 2x\left(-x-\cot\left(x\right)\right)+x^2+2\ln\left(\sin\left(x\right)\right). Gather the results of all integrals. The integral \int x^2dx results in: \frac{x^{3}}{3}.

Final Answer

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

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 (2x+x^2)dx using basic integralsSolve integral of (2x+x^2)dx using u-substitutionSolve integral of (2x+x^2)dx using integration by partsSolve integral of (2x+x^2)dx using tabular integration

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0
a
b
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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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

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