Solve the trigonometric integral $\int\frac{d\infty}{1+\cos\left(\\right)infty}d\$

Step-by-step Solution

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Final answer to the problem

$\frac{2d\infty\arctan\left(\frac{\tan\left(\frac{\}{2}\right)}{\sqrt{1+\left(1- \tan\left(\frac{\}{2}\right)^{2}\right)infty}}\right)}{\sqrt{1+\left(1- \tan\left(\frac{\}{2}\right)^{2}\right)infty}}+C_0$
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Step-by-step Solution

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  • 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
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The integral of a function times a constant ($d\infty$) is equal to the constant times the integral of the function

$d\infty\int\frac{1}{1+\cos\left(\\right)infty}d\$

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$d\infty\int\frac{1}{1+\cos\left(\\right)infty}d\$

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Learn how to solve rational equations problems step by step online. Solve the trigonometric integral int(d\infty/(1+cos(\)infty))d\. The integral of a function times a constant (d\infty) is equal to the constant times the integral of the function. We can solve the integral \int\frac{1}{1+\cos\left(\\right)infty}d\ 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.

Final answer to the problem

$\frac{2d\infty\arctan\left(\frac{\tan\left(\frac{\}{2}\right)}{\sqrt{1+\left(1- \tan\left(\frac{\}{2}\right)^{2}\right)infty}}\right)}{\sqrt{1+\left(1- \tan\left(\frac{\}{2}\right)^{2}\right)infty}}+C_0$

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Function Plot

Plotting: $\frac{2d\infty\arctan\left(\frac{\tan\left(\frac{\}{2}\right)}{\sqrt{1+\left(1- \tan\left(\frac{\}{2}\right)^{2}\right)infty}}\right)}{\sqrt{1+\left(1- \tan\left(\frac{\}{2}\right)^{2}\right)infty}}+C_0$

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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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