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Solve the trigonometric integral $\int\frac{1}{4+5\cos\left(x\right)}dx$

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Solution

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Final answer to the problem

$\frac{1}{3}\ln\left(3\right)+C_1$
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Learn how to solve weierstrass substitution problems step by step online. Solve the trigonometric integral int(1/(4+5cos(x)))dx. We can solve the integral \int\frac{1}{4+5\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 to the problem

$\frac{1}{3}\ln\left(3\right)+C_1$

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Function Plot

Plotting: $\frac{1}{3}\ln\left(3\right)+C_1$

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x
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(◻)
+
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◻/◻
/
÷
◻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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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

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