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# Solve the trigonometric integral $\int2\sin\left(x\right)\cos\left(x\right)^2dx$

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##  Final answer to the problem

$-\frac{2}{3}\cos\left(x\right)^{3}+C_0$
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##  Step-by-step Solution 

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The integral of a function times a constant ($2$) is equal to the constant times the integral of the function

$2\int\sin\left(x\right)\cos\left(x\right)^2dx$

Learn how to solve integral calculus problems step by step online.

$2\int\sin\left(x\right)\cos\left(x\right)^2dx$

Learn how to solve integral calculus problems step by step online. Solve the trigonometric integral int(2sin(x)cos(x)^2)dx. 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\sin\left(x\right)\cos\left(x\right)^2dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that \cos\left(x\right) it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation.

##  Final answer to the problem

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

##  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 2sinxdx using basic integralsSolve integral of 2sinxdx using u-substitutionSolve integral of 2sinxdx using integration by partsIntegrate using trigonometric identitiesSolve integral of 2sinxdx using weierstrass substitution

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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

###  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.