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

Step-by-step Solution

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Final Answer

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

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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.

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

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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.

Final Answer

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

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

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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

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