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Solve the trigonometric integral $\int\mathrm{coth}\left(x\right)dx$

Step-by-step Solution

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Solution

Formulas

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Final answer to the problem

$\ln\left|\mathrm{sinh}\left(x\right)\right|+C_0$
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Step-by-step Solution

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  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
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We can solve the integral $\int\mathrm{coth}\left(x\right)dx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

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

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

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Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(coth(x))dx. We can solve the integral \int\mathrm{coth}\left(x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v. Solve the integral to find v.

Final answer to the problem

$\ln\left|\mathrm{sinh}\left(x\right)\right|+C_0$

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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

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Function Plot

Plotting: $\ln\left(\mathrm{sinh}\left(x\right)\right)+C_0$

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Got a different answer? Verify it!

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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
D□x
∫
∫◻
|◻|
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

How to improve your answer:

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Main Topic: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.

Used Formulas

See formulas (6)

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