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Solve the trigonometric integral $\int\cos\left(4x\right)\cos\left(3x\right)dx$

Step-by-step Solution

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Final Answer

$\frac{1}{14}\sin\left(7x\right)+\frac{1}{2}\sin\left(x\right)+C_0$
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Step-by-step Solution

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Apply the rule of the product of two cosines $\cos\left(a\right)\cdot\cos\left(b\right)=\frac{\cos\left(a+b\right)+\cos\left(a-b\right)}{2}$

$\int\frac{\cos\left(7x\right)+\cos\left(x\right)}{2}dx$

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

$\int\frac{\cos\left(7x\right)+\cos\left(x\right)}{2}dx$

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Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(cos(4x)cos(3x))dx. Apply the rule of the product of two cosines \cos\left(a\right)\cdot\cos\left(b\right)=\frac{\cos\left(a+b\right)+\cos\left(a-b\right)}{2}. Take the constant \frac{1}{2} out of the integral. Simplify the expression inside the integral. We can solve the integral \int\cos\left(x\right)dx by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution.

Final Answer

$\frac{1}{14}\sin\left(7x\right)+\frac{1}{2}\sin\left(x\right)+C_0$

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Function Plot

Plotting: $\frac{1}{14}\sin\left(7x\right)+\frac{1}{2}\sin\left(x\right)+C_0$

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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

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