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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of e^(3*x)
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Integral of 1/(x^3)
- Integral of |x|
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Integral of -2x
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Identical expressions
- xsin(ax)dx
- x sinus of (ax)dx
- xsinaxdx
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Similar expressions
- x*sin(a*x)*dx
Integral of xsin(ax)dx dx
The solution
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[src]
1 / | | x*sin(a*x) dx | / 0
$$\int\limits_{0}^{1} x \sin{\left(a x \right)}\, dx$$
Integral(x*sin(a*x), (x, 0, 1))
The answer (Indefinite)
[src]
// 0 for a = 0\
|| |
/ || //sin(a*x) \ | // 0 for a = 0\
| || ||-------- for a != 0| | || |
| x*sin(a*x) dx = C - |<-|< a | | + x*|<-cos(a*x) |
| || || | | ||---------- otherwise|
/ || \\ x otherwise / | \\ a /
||------------------------- otherwise|
\\ a /
$$\int x \sin{\left(a x \right)}\, dx = C + x \left(\begin{cases} 0 & \text{for}\: a = 0 \\- \frac{\cos{\left(a x \right)}}{a} & \text{otherwise} \end{cases}\right) - \begin{cases} 0 & \text{for}\: a = 0 \\- \frac{\begin{cases} \frac{\sin{\left(a x \right)}}{a} & \text{for}\: a \neq 0 \\x & \text{otherwise} \end{cases}}{a} & \text{otherwise} \end{cases}$$
The answer
[src]
/sin(a) cos(a) |------ - ------ for And(a > -oo, a < oo, a != 0) | 2 a < a | | 0 otherwise \
$$\begin{cases} - \frac{\cos{\left(a \right)}}{a} + \frac{\sin{\left(a \right)}}{a^{2}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/sin(a) cos(a) |------ - ------ for And(a > -oo, a < oo, a != 0) | 2 a < a | | 0 otherwise \
$$\begin{cases} - \frac{\cos{\left(a \right)}}{a} + \frac{\sin{\left(a \right)}}{a^{2}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((sin(a)/a^2 - cos(a)/a, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (0, True))
Use the examples entering the upper and lower limits of integration.