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# Solve the trigonometric integral $\int\cos\left(\frac{1}{2}x\right)dx$

## Step-by-step Solution

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###  Videos

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

Problem to solve:

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

Specify the solving method

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We can solve the integral $\int\cos\left(\frac{1}{2}x\right)dx$ 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 $\frac{1}{2}x$ it's a good candidate for substitution. Let's define a variable $u$ and assign it to the choosen part

$u=\frac{1}{2}x$

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

$u=\frac{1}{2}x$

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(cos(1/2x))dx. We can solve the integral \int\cos\left(\frac{1}{2}x\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 \frac{1}{2}x 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. Substituting u and dx in the integral and simplify.

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

##  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 integral of cos0.5xdx using basic integralsSolve integral of cos0.5xdx using u-substitutionSolve integral of cos0.5xdx using integration by partsSolve integral of cos0.5xdx using tabular integrationSolve integral of cos0.5xdx using weierstrass substitution

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5
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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

### Main topic:

Trigonometric Integrals

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