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# Solve the trigonometric integral $\int\frac{1}{1+\sin\left(\theta\right)+\cos\left(\theta\right)}dt$

## Step-by-step Solution

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Solving: $\int\frac{1}{1+\sin\left(t\right)+\cos\left(t\right)}dt$

##  Final answer to the problem

$\ln\left|\tan\left(\frac{\theta}{2}\right)+1\right|+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• 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
Can't find a method? Tell us so we can add it.
1

We can solve the integral $\int\frac{1}{1+\sin\left(\theta\right)+\cos\left(\theta\right)}dt$ 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 $\theta$ by setting the substitution

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

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

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

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(1/(1+sin(t)cos(t)))dt. We can solve the integral \int\frac{1}{1+\sin\left(\theta\right)+\cos\left(\theta\right)}dt 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 \theta by setting the substitution. Hence. Substituting in the original integral we get. Simplifying.

##  Final answer to the problem

$\ln\left|\tan\left(\frac{\theta}{2}\right)+1\right|+C_0$

##  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

SnapXam A2

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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

###  Main Topic: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.