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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 xcosnx
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Integral of ctg²x
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Integral of x/(sqrt(2x+7))
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Integral of arccos(3x)/(sqrt(1-9x^2))
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Identical expressions
- xcosnx
- x co sinus of e of nx
- xcosnxdx
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Similar expressions
- x*cos(nx)
- sin(mx)cos(nx)
- e^(2x)*cos(nx)
- sin(x)*cos(nx)
Integral of xcosnx dx
The solution
You have entered
[src]
1 / | | x*cos(n*x) dx | / 0
$$\int\limits_{0}^{1} x \cos{\left(n x \right)}\, dx$$
The answer (Indefinite)
[src]
// 2 \
|| x |
|| -- for n = 0|
|| 2 |
/ || | // x for n = 0\
| ||/-cos(n*x) | || |
| x*cos(n*x) dx = C - |<|---------- for n != 0 | + x*|
$${{n\,x\,\sin \left(n\,x\right)+\cos \left(n\,x\right)}\over{n^2}}$$
The answer
[src]
/ 1 sin(n) cos(n) |- -- + ------ + ------ for And(n > -oo, n < oo, n != 0) | 2 n 2 < n n | | 1/2 otherwise \
$${{n\,\sin n+\cos n}\over{n^2}}-{{1}\over{n^2}}$$
=
=
/ 1 sin(n) cos(n) |- -- + ------ + ------ for And(n > -oo, n < oo, n != 0) | 2 n 2 < n n | | 1/2 otherwise \
$$\begin{cases} \frac{\sin{\left(n \right)}}{n} + \frac{\cos{\left(n \right)}}{n^{2}} - \frac{1}{n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{1}{2} & \text{otherwise} \end{cases}$$
Use the examples entering the upper and lower limits of integration.