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