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Solve the trigonometric integral $\int\frac{1}{\cos\left(u\right)-1}du$

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Solution

Formulas

Videos

Integral of 1/e^x

https://www.youtube.com/watch?v=LZf8mMxE3l4

Pre-Calculus - Determining the triple angle of cosine to solve the equation cos(3x)=-1/2

https://www.youtube.com/watch?v=M4ZbUoyVWvE

Integral of 1/sqrt(1-x^2)

https://www.youtube.com/watch?v=9AvyXgfNN9E

integral of arcsin x

https://www.youtube.com/watch?v=qwHhwdvTGdY

Integral of Cos(2x)

https://www.youtube.com/watch?v=cCdj0uy0v80

Use u substitution with trigonometric functions

https://www.youtube.com/watch?v=JHQFYsswbNU

Function Plot

Plotting: $\frac{1}{\tan\left(\frac{u}{2}\right)}+C_0$

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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
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

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Similar Problems Solved

Find the integral

$\int\frac{1}{1-sin\left(x\right)}dx$

Find the integral

$\int\frac{dx}{1-sin\left(x\right)}$

Find the integral

$\int\frac{1}{1-sinx}dx$

Find the integral

$\int\frac{1}{cosx-1}dx$

Find the integral

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

Find the integral

$\int\frac{1}{\sin\left(x\right)-1}dx$

Find the integral

$\int\frac{dx}{1-\sin\left(x\right)}$

Main Topic: Weierstrass Substitution

In integral calculus, the Weierstrass substitution or tangent half angle substitution is a method for solving integrals, which converts a rational expression of trigonometric functions into an algebraic rational function, which can be easier to integrate. The Weierstrass substitution is very useful for integrals that involve a simple rational expression with sine and/or cosine in the denominator.

Used Formulas

See formulas (2)

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