ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Solve the trigonometric integral $\int\cos\left(100x+200\right)dx$

## Step-by-step Solution

Go!
Math mode
Text mode
Go!
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

###  Videos

$\frac{1}{100}\sin\left(100x+200\right)+C_0$
Got another answer? Verify it here!

##  Step-by-step Solution 

Specify the solving method

1

We can solve the integral $\int\cos\left(100x+200\right)dx$ 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 $100x+200$ it's a good candidate for substitution. Let's define a variable $u$ and assign it to the choosen part

$u=100x+200$

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

$u=100x+200$

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(cos(100x+200))dx. We can solve the integral \int\cos\left(100x+200\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 100x+200 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.

$\frac{1}{100}\sin\left(100x+200\right)+C_0$

##  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 cos(100x+200)dx using basic integralsSolve integral of cos(100x+200)dx using u-substitutionSolve integral of cos(100x+200)dx using integration by partsSolve integral of cos(100x+200)dx using tabular integration

SnapXam A2

Go!
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.

###  Join 500k+ students in problem solving.

##### Without automatic renewal.
Create an Account