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Solve the trigonometric integral $\int\cos\left(4x\right)\cos\left(6x\right)dx$

Step-by-step Solution

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Final Answer

$\frac{1}{20}\sin\left(10x\right)+\frac{1}{4}\sin\left(2x\right)+C_0$
Got another answer? Verify it here!

Step-by-step Solution

Problem to solve:

$\int\cos\left(4x\right)\cdot\cos\left(6x\right)dx$

Specify the solving method

1

Rewrite the trigonometric expression $\cos\left(4x\right)\cos\left(6x\right)$ inside the integral

$\int\frac{\cos\left(10x\right)+\cos\left(2x\right)}{2}dx$
2

Take the constant $\frac{1}{2}$ out of the integral

$\frac{1}{2}\int\left(\cos\left(10x\right)+\cos\left(2x\right)\right)dx$

Learn how to solve trigonometric integrals problems step by step online.

$\int\frac{\cos\left(10x\right)+\cos\left(2x\right)}{2}dx$

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Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(cos(4x)cos(6x))dx. Rewrite the trigonometric expression \cos\left(4x\right)\cos\left(6x\right) inside the integral. Take the constant \frac{1}{2} out of the integral. Expand the integral \int\left(\cos\left(10x\right)+\cos\left(2x\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \frac{1}{2}\int\cos\left(10x\right)dx results in: \frac{1}{20}\sin\left(10x\right).

Final Answer

$\frac{1}{20}\sin\left(10x\right)+\frac{1}{4}\sin\left(2x\right)+C_0$

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

Solve int(cos(4x)cos(6x))dx using basic integralsSolve int(cos(4x)cos(6x))dx using u-substitutionSolve int(cos(4x)cos(6x))dx using integration by partsSolve int(cos(4x)cos(6x))dx using weierstrass substitution
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Got a different answer? Verify it!

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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

How to improve your answer:

$\int\cos\left(4x\right)\cdot\cos\left(6x\right)dx$

Used formulas:

4. See formulas

Time to solve it:

~ 0.09 s