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# Find the integral $\frac{1}{9}\int\frac{1}{\cos\left(2x\right)}dx$

## Step-by-step Solution

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sinh
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asinh
acosh
atanh
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asech
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### Videos

$\frac{1}{18}\ln\left(\sec\left(2x\right)+\tan\left(2x\right)\right)+C_0$
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## Step-by-step Solution

Problem to solve:

$\int\frac{1}{\cos\left(2x\right)}dx\cdot\frac{1}{9}$

Specify the solving method

1

Simplify $\sec\left(2x\right)$ by applying trigonometric identities

$\frac{1}{9}\int\sec\left(2x\right)dx$

Learn how to solve integration by substitution problems step by step online.

$\frac{1}{9}\int\sec\left(2x\right)dx$

Learn how to solve integration by substitution problems step by step online. Find the integral int(1/(cos(2x))dx1/9. Simplify \sec\left(2x\right) by applying trigonometric identities. We can solve the integral \int\sec\left(2x\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 2x 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.

$\frac{1}{18}\ln\left(\sec\left(2x\right)+\tan\left(2x\right)\right)+C_0$
SnapXam A2

Go!
1
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5
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7
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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

### Useful tips on how to improve your answer:

$\int\frac{1}{\cos\left(2x\right)}dx\cdot\frac{1}{9}$

### Main topic:

Integration by Substitution

~ 0.04 s