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

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##  Final Answer

$\frac{-\cos\left(2ax\right)}{4a}+C_0$
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##  Step-by-step Solution 

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Simplify $\sin\left(ax\right)\cos\left(ax\right)$ into $\frac{1}{2}\sin\left(2ax\right)$ by applying trigonometric identities

$\int\frac{1}{2}\sin\left(2ax\right)dx$

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

$\int\frac{1}{2}\sin\left(2ax\right)dx$

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sin(ax)cos(ax))dx. Simplify \sin\left(ax\right)\cos\left(ax\right) into \frac{1}{2}\sin\left(2ax\right) by applying trigonometric identities. The integral of a function times a constant (\frac{1}{2}) is equal to the constant times the integral of the function. We can solve the integral \int\sin\left(2ax\right)dx 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 2ax 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.

##  Final Answer

$\frac{-\cos\left(2ax\right)}{4a}+C_0$

##  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 sinaxcosaxdx using basic integralsSolve integral of sinaxcosaxdx using u-substitutionSolve integral of sinaxcosaxdx using integration by partsSolve integral of sinaxcosaxdx using weierstrass substitution

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1
2
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: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.

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