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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 8dx
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Integral of x/sqrt(x^2-1)
- Integral of sinh^-1x
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Integral of ctg^2x
- The double integral of:
- ycos(xy)
- ycos(xy)
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Identical expressions
- ycos(xy)
- y co sinus of e of (xy)
- ycosxy
- ycos(xy)dx
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Similar expressions
- y*((y*cos(x))*(y*sin(x)))
Integral of ycos(xy) dy
The solution
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pi / | | y*cos(x*y) dy | / 0
$$\int\limits_{0}^{\pi} y \cos{\left(x y \right)}\, dy$$
Integral(y*cos(x*y), (y, 0, pi))
The answer (Indefinite)
[src]
// 2 \
|| y |
|| -- for x = 0|
|| 2 |
/ || | // y for x = 0\
| ||/-cos(x*y) | || |
| y*cos(x*y) dy = C - |<|---------- for x != 0 | + y*|
$$\int y \cos{\left(x y \right)}\, dy = C + y \left(\begin{cases} y & \text{for}\: x = 0 \\\frac{\sin{\left(x y \right)}}{x} & \text{otherwise} \end{cases}\right) - \begin{cases} \frac{y^{2}}{2} & \text{for}\: x = 0 \\\frac{\begin{cases} - \frac{\cos{\left(x y \right)}}{x} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}}{x} & \text{otherwise} \end{cases}$$
The answer
[src]
/ 1 cos(pi*x) pi*sin(pi*x) |- -- + --------- + ------------ for And(x > -oo, x < oo, x != 0) | 2 2 x | x x < | 2 | pi | --- otherwise \ 2
$$\begin{cases} \frac{\pi \sin{\left(\pi x \right)}}{x} + \frac{\cos{\left(\pi x \right)}}{x^{2}} - \frac{1}{x^{2}} & \text{for}\: x > -\infty \wedge x < \infty \wedge x \neq 0 \\\frac{\pi^{2}}{2} & \text{otherwise} \end{cases}$$
=
=
/ 1 cos(pi*x) pi*sin(pi*x) |- -- + --------- + ------------ for And(x > -oo, x < oo, x != 0) | 2 2 x | x x < | 2 | pi | --- otherwise \ 2
$$\begin{cases} \frac{\pi \sin{\left(\pi x \right)}}{x} + \frac{\cos{\left(\pi x \right)}}{x^{2}} - \frac{1}{x^{2}} & \text{for}\: x > -\infty \wedge x < \infty \wedge x \neq 0 \\\frac{\pi^{2}}{2} & \text{otherwise} \end{cases}$$
Piecewise((-1/x^2 + cos(pi*x)/x^2 + pi*sin(pi*x)/x, (x > -oo)∧(x < oo)∧(Ne(x, 0))), (pi^2/2, True))
Use the examples entering the upper and lower limits of integration.