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# Solve the trigonometric integral $\int\csc\left(x\right)dx$

## Step-by-step Solution

Go!
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e
π
ln
log
log
lim
d/dx
Dx
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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

$-\ln\left(\csc\left(x\right)+\cot\left(x\right)\right)+C_0$
Got another answer? Verify it here!

## Step-by-step Solution

Problem to solve:

$\int\csc\left(x\right)dx$

Specify the solving method

1

The integral of $\csc(x)$ is $-\ln(\csc(x)+\cot(x))$

$-\ln\left(\csc\left(x\right)+\cot\left(x\right)\right)$
2

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$-\ln\left(\csc\left(x\right)+\cot\left(x\right)\right)+C_0$

$-\ln\left(\csc\left(x\right)+\cot\left(x\right)\right)+C_0$

##  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 int(csc(x))dx using basic integralsSolve int(csc(x))dx using u-substitutionSolve int(csc(x))dx using integration by partsSolve int(csc(x))dx using tabular integrationSolve int(csc(x))dx using weierstrass substitution
SnapXam A2

### beta Got a different answer? Verify it!

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

$\int\csc\left(x\right)dx$

### Main topic:

Trigonometric Integrals

~ 0.02 s