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

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##  Final answer to the problem

$-\frac{1}{8}\cos\left(4x\right)+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
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Simplify $\sin\left(2x\right)\cos\left(2x\right)$ into $\frac{\sin\left(4x\right)}{2}$ by applying trigonometric identities

$\int\frac{\sin\left(4x\right)}{2}dx$

Learn how to solve limits by direct substitution problems step by step online.

$\int\frac{\sin\left(4x\right)}{2}dx$

Learn how to solve limits by direct substitution problems step by step online. Solve the trigonometric integral int(sin(2x)cos(2x))dx. Simplify \sin\left(2x\right)\cos\left(2x\right) into \frac{\sin\left(4x\right)}{2} by applying trigonometric identities. Take the constant \frac{1}{2} out of the integral. Apply the formula: \int\sin\left(ax\right)dx=-\left(\frac{1}{a}\right)\cos\left(ax\right)+C, where a=4. Simplify the expression.

##  Final answer to the problem

$-\frac{1}{8}\cos\left(4x\right)+C_0$

##  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

SnapXam A2

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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

###  Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.