👉 Try now NerdPal! Our new math app on iOS and Android

Solve the trigonometric integral $\int\frac{1}{1-\sin\left(o\right)}do$

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

Final Answer

$\frac{-2}{\tan\left(\frac{o}{2}\right)-1}+C_0$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

1

We can solve the integral $\int\frac{1}{1-\sin\left(o\right)}do$ by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of $t$ by setting the substitution

$t=\tan\left(\frac{o}{2}\right)$

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

$t=\tan\left(\frac{o}{2}\right)$

Unlock unlimited step-by-step solutions and much more!

Unlock the first 2 steps of this solution.

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(1/(1-sin(o)))do. We can solve the integral \int\frac{1}{1-\sin\left(o\right)}do by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution. Hence. Substituting in the original integral we get. Simplifying.

Final Answer

$\frac{-2}{\tan\left(\frac{o}{2}\right)-1}+C_0$

Explore different ways to solve this problem

Give us your feedback!

Function Plot

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

SnapXam A2
Answer Assistant

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

How to improve your answer:

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your Subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account