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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x*e^(x*(-2))
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Integral of x^3(e^x^2)
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Integral of (x^3-1)^1/2
- Integral of e^(a*x)*sin(b*x)*dx
- Graphing y =:
- x*cos(1/x)
- Limit of the function:
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x*cos(1/x)
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Identical expressions
- x*cos(one /x)
- x multiply by co sinus of e of (1 divide by x)
- x multiply by co sinus of e of (one divide by x)
- xcos(1/x)
- xcos1/x
- x*cos(1 divide by x)
- x*cos(1/x)dx
Integral of x*cos(1/x) dx
The solution
You have entered
[src]
1 / | | /1\ | x*cos|-| dx | \x/ | / 0
$$\int\limits_{0}^{1} x \cos{\left(\frac{1}{x} \right)}\, dx$$
Integral(x*cos(1/x), (x, 0, 1))
The answer (Indefinite)
[src]
/1 \ / /1\ /1\ log|--| 2 /1\ /1\ | Ci|-| log|-| | 2| x *cos|-| x*sin|-| | /1\ \x/ \x/ \x / \x/ \x/ | x*cos|-| dx = C + ----- - ------ + ------- + --------- - -------- | \x/ 2 2 4 2 2 | /
$$\int x \cos{\left(\frac{1}{x} \right)}\, dx = C + \frac{x^{2} \cos{\left(\frac{1}{x} \right)}}{2} - \frac{x \sin{\left(\frac{1}{x} \right)}}{2} + \frac{\log{\left(\frac{1}{x^{2}} \right)}}{4} - \frac{\log{\left(\frac{1}{x} \right)}}{2} + \frac{\operatorname{Ci}{\left(\frac{1}{x} \right)}}{2}$$
The graph
The answer
[src]
Ci(1) cos(1) sin(1) ----- + ------ - ------ 2 2 2
$$- \frac{\sin{\left(1 \right)}}{2} + \frac{\operatorname{Ci}{\left(1 \right)}}{2} + \frac{\cos{\left(1 \right)}}{2}$$
=
=
Ci(1) cos(1) sin(1) ----- + ------ - ------ 2 2 2
$$- \frac{\sin{\left(1 \right)}}{2} + \frac{\operatorname{Ci}{\left(1 \right)}}{2} + \frac{\cos{\left(1 \right)}}{2}$$
Ci(1)/2 + cos(1)/2 - sin(1)/2
Use the examples entering the upper and lower limits of integration.