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