Mister Exam
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- Improper integral
- Double Integral
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- Curvilinear integral
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How to use it?
- Integral of d{x}:
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Integral of e^(-x^2)
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Integral of e^x^2
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Integral of e^2
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Integral of 2/x^2
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Identical expressions
- xsinnx
- x sinus of nx
- xsinnxdx
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Similar expressions
- sin(x)*sin(nx)
- sin(x)*sin(n*x)
- x*sin(n*x)*dx
- (4-9x)*sin(nx)
Integral of xsinnx dx
The solution
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[src]
1 / | | x*sin(n*x) dx | / 0
$$\int\limits_{0}^{1} x \sin{\left(n x \right)}\, dx$$
Integral(x*sin(n*x), (x, 0, 1))
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(n) cos(n) |------ - ------ for And(n > -oo, n < oo, n != 0) | 2 n < n | | 0 otherwise \
$$\begin{cases} - \frac{\cos{\left(n \right)}}{n} + \frac{\sin{\left(n \right)}}{n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/sin(n) cos(n) |------ - ------ for And(n > -oo, n < oo, n != 0) | 2 n < n | | 0 otherwise \
$$\begin{cases} - \frac{\cos{\left(n \right)}}{n} + \frac{\sin{\left(n \right)}}{n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((sin(n)/n^2 - cos(n)/n, (n > -oo)∧(n < oo)∧(Ne(n, 0))), (0, True))
Use the examples entering the upper and lower limits of integration.