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How to use it?
- Integral of d{x}:
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Integral of e^-x
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Integral of e^x/x
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Integral of 1/sin²(x)
- Integral of sqrt(1+x)/sqrt(1-x)
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Identical expressions
- x*cos(nx)
- x multiply by co sinus of e of (nx)
- xcos(nx)
- xcosnx
- x*cos(nx)dx
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Similar expressions
- sinxcosnx
- sin^2(x)cos(nx)
- e^(2x)*cos(nx)
- (pi+2x)cos(nx)
- sin(x)*cos(nx)
Integral of x*cos(nx) dx
The solution
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[src]
1 / | | x*cos(n*x) dx | / 0
$$\int\limits_{0}^{1} x \cos{\left(n x \right)}\, dx$$
Integral(x*cos(n*x), (x, 0, 1))
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.