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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of cos3x
- Integral of xsin(kx)
- Integral of x^4/(x^2+a^2)
- Integral of x-2y
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Identical expressions
- xsin(kx)
- x sinus of (kx)
- xsinkx
- xsin(kx)dx
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Similar expressions
- sin(x)sin(kx)
- x*sin(kx)
- (4-2*x)*sin(kx)
- 2x*sin(kx)
- X*sinx*sinkx
Integral of xsin(kx) dx
The solution
You have entered
[src]
1 / | | x*sin(k*x) dx | / 0
$$\int\limits_{0}^{1} x \sin{\left(k x \right)}\, dx$$
Integral(x*sin(k*x), (x, 0, 1))
The answer (Indefinite)
[src]
// 0 for k = 0\
|| |
/ || //sin(k*x) \ | // 0 for k = 0\
| || ||-------- for k != 0| | || |
| x*sin(k*x) dx = C - |<-|< k | | + x*|<-cos(k*x) |
| || || | | ||---------- otherwise|
/ || \\ x otherwise / | \\ k /
||------------------------- otherwise|
\\ k /
$${{\sin \left(k\,x\right)-k\,x\,\cos \left(k\,x\right)}\over{k^2}}$$
The answer
[src]
/sin(k) cos(k) |------ - ------ for And(k > -oo, k < oo, k != 0) | 2 k < k | | 0 otherwise \
$${{\sin k-k\,\cos k}\over{k^2}}$$
=
=
/sin(k) cos(k) |------ - ------ for And(k > -oo, k < oo, k != 0) | 2 k < k | | 0 otherwise \
$$\begin{cases} - \frac{\cos{\left(k \right)}}{k} + \frac{\sin{\left(k \right)}}{k^{2}} & \text{for}\: k > -\infty \wedge k < \infty \wedge k \neq 0 \\0 & \text{otherwise} \end{cases}$$
Use the examples entering the upper and lower limits of integration.