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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
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How to use it?
- Integral of d{x}:
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Integral of 2x(x^2+1)
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Integral of (1+2x^2)/(x^2(1+x^2))
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Integral of 1/(2+cosx)^2
- Integral of x/((x-1)(x-2))
- The double integral of:
- y*sin(2xy)
- y*sin(2xy)
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Identical expressions
- y*sin(2xy)
- y multiply by sinus of (2xy)
- ysin(2xy)
- ysin2xy
- y*sin(2xy)dx
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Similar expressions
- 12*y*sin(2*x*y)
- 2(exp((x^2)-(y^2)))*(x(cos(2xy))-ysin(2xy))
Integral of y*sin(2xy) dy
The solution
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[src]
1 / | | y*sin(2*x*y) dy | / 0
$$\int\limits_{0}^{1} y \sin{\left(2 x y \right)}\, dy$$
Integral(y*sin((2*x)*y), (y, 0, 1))
The answer (Indefinite)
[src]
// 0 for x = 0\
|| |
/ || //sin(2*x*y) \ | // 0 for x = 0\
| || ||---------- for 2*x != 0| | || |
| y*sin(2*x*y) dy = C - |<-|< 2*x | | + y*|<-cos(2*x*y) |
| || || | | ||------------ otherwise|
/ || \\ y otherwise / | \\ 2*x /
||----------------------------- otherwise|
\\ 2*x /
$$\int y \sin{\left(2 x y \right)}\, dy = C + y \left(\begin{cases} 0 & \text{for}\: x = 0 \\- \frac{\cos{\left(2 x y \right)}}{2 x} & \text{otherwise} \end{cases}\right) - \begin{cases} 0 & \text{for}\: x = 0 \\- \frac{\begin{cases} \frac{\sin{\left(2 x y \right)}}{2 x} & \text{for}\: 2 x \neq 0 \\y & \text{otherwise} \end{cases}}{2 x} & \text{otherwise} \end{cases}$$
The answer
[src]
/ cos(2*x) sin(2*x) |- -------- + -------- for And(x > -oo, x < oo, x != 0) | 2*x 2 < 4*x | | 0 otherwise \
$$\begin{cases} - \frac{\cos{\left(2 x \right)}}{2 x} + \frac{\sin{\left(2 x \right)}}{4 x^{2}} & \text{for}\: x > -\infty \wedge x < \infty \wedge x \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/ cos(2*x) sin(2*x) |- -------- + -------- for And(x > -oo, x < oo, x != 0) | 2*x 2 < 4*x | | 0 otherwise \
$$\begin{cases} - \frac{\cos{\left(2 x \right)}}{2 x} + \frac{\sin{\left(2 x \right)}}{4 x^{2}} & \text{for}\: x > -\infty \wedge x < \infty \wedge x \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((-cos(2*x)/(2*x) + sin(2*x)/(4*x^2), (x > -oo)∧(x < oo)∧(Ne(x, 0))), (0, True))
Use the examples entering the upper and lower limits of integration.