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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
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How to use it?
- Integral of d{x}:
- Integral of (x+6)x+67x!
- Integral of sin(x)^2/(1-tan(x))
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Integral of (5x^3+2)/(x^3-5x^2+4x)
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Integral of (4-x^2)^2
- Graphing y =:
- cos(2*x)/((2*x))
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Identical expressions
- cos(two *x)/((two *x))
- co sinus of e of (2 multiply by x) divide by ((2 multiply by x))
- co sinus of e of (two multiply by x) divide by ((two multiply by x))
- cos(2x)/((2x))
- cos2x/2x
- cos(2*x) divide by ((2*x))
- cos(2*x)/((2*x))dx
Integral of cos(2*x)/((2*x)) dx
The solution
You have entered
[src]
oo / | | cos(2*x) | -------- dx | 2*x | / 0
$$\int\limits_{0}^{\infty} \frac{\cos{\left(2 x \right)}}{2 x}\, dx$$
Integral(cos(2*x)/((2*x)), (x, 0, oo))
Detail solution
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Let .
Then let and substitute :
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The integral of a constant times a function is the constant times the integral of the function:
CiRule(a=1, b=0, context=cos(_u)/_u, symbol=_u)
So, the result is:
Now substitute back in:
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Add the constant of integration:
The answer is:
The answer (Indefinite)
[src]
/ | | cos(2*x) Ci(2*x) | -------- dx = C + ------- | 2*x 2 | /
$$\int \frac{\cos{\left(2 x \right)}}{2 x}\, dx = C + \frac{\operatorname{Ci}{\left(2 x \right)}}{2}$$
The graph
The answer
[src]
oo
/
|
| cos(2*x)
| -------- dx
| x
|
/
0
---------------
2
$$\frac{\int\limits_{0}^{\infty} \frac{\cos{\left(2 x \right)}}{x}\, dx}{2}$$
=
=
oo
/
|
| cos(2*x)
| -------- dx
| x
|
/
0
---------------
2
$$\frac{\int\limits_{0}^{\infty} \frac{\cos{\left(2 x \right)}}{x}\, dx}{2}$$
Integral(cos(2*x)/x, (x, 0, oo))/2
Use the examples entering the upper and lower limits of integration.