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The solution
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[src]
180 / | | x*sin(n*x) dx | / 0
$$\int\limits_{0}^{180} x \sin{\left(n x \right)}\, dx$$
Integral(x*sin(n*x), (x, 0, 180))
The answer (Indefinite)
[src]
// 0 for n = 0\
|| |
/ || //sin(n*x) \ | // 0 for n = 0\
| || ||-------- for n != 0| | || |
| x*sin(n*x) dx = C - |<-|< n | | + x*|<-cos(n*x) |
| || || | | ||---------- otherwise|
/ || \\ x otherwise / | \\ n /
||------------------------- otherwise|
\\ n /
$$\int x \sin{\left(n x \right)}\, dx = C + x \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\cos{\left(n x \right)}}{n} & \text{otherwise} \end{cases}\right) - \begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\begin{cases} \frac{\sin{\left(n x \right)}}{n} & \text{for}\: n \neq 0 \\x & \text{otherwise} \end{cases}}{n} & \text{otherwise} \end{cases}$$
The answer
[src]
/sin(180*n) 180*cos(180*n) |---------- - -------------- for And(n > -oo, n < oo, n != 0) | 2 n < n | | 0 otherwise \
$$\begin{cases} - \frac{180 \cos{\left(180 n \right)}}{n} + \frac{\sin{\left(180 n \right)}}{n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/sin(180*n) 180*cos(180*n) |---------- - -------------- for And(n > -oo, n < oo, n != 0) | 2 n < n | | 0 otherwise \
$$\begin{cases} - \frac{180 \cos{\left(180 n \right)}}{n} + \frac{\sin{\left(180 n \right)}}{n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((sin(180*n)/n^2 - 180*cos(180*n)/n, (n > -oo)∧(n < oo)∧(Ne(n, 0))), (0, True))
Use the examples entering the upper and lower limits of integration.