ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Solve the trigonometric integral $\int\frac{5\sin\left(x\right)}{1-\cos\left(x\right)}dx$

## 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

###  Solution

$-5\ln\left(\sec\left(\frac{x}{2}\right)^2\right)+10\ln\left(\tan\left(\frac{x}{2}\right)\right)+C_0$
Got another answer? Verify it here!

##  Step-by-step Solution 

Specify the solving method

1

We can solve the integral $\int\frac{5\sin\left(x\right)}{1-\cos\left(x\right)}dx$ 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

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

Learn how to solve differential calculus problems step by step online.

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

Learn how to solve differential calculus problems step by step online. Solve the trigonometric integral int((5sin(x))/(1-cos(x)))dx. We can solve the integral \int\frac{5\sin\left(x\right)}{1-\cos\left(x\right)}dx 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.

$-5\ln\left(\sec\left(\frac{x}{2}\right)^2\right)+10\ln\left(\tan\left(\frac{x}{2}\right)\right)+C_0$

##  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 integral of (5sinx/(1+-1cosx))dx using basic integralsSolve integral of (5sinx/(1+-1cosx))dx using u-substitutionSolve integral of (5sinx/(1+-1cosx))dx using integration by parts

SnapXam A2

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

###  Join 500k+ students in problem solving.

##### Without automatic renewal.
Create an Account