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- Integral of d{x}:
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Integral of x^2*e^(x*(-2))
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Integral of e^(-x^3)
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Integral of -exp(-3*x)
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Integral of -x^-2
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Identical expressions
- (two / three (x- one))cos(nx)
- (2 divide by 3(x minus 1)) co sinus of e of (nx)
- (two divide by three (x minus one)) co sinus of e of (nx)
- 2/3x-1cosnx
- (2 divide by 3(x-1))cos(nx)
- (2/3(x-1))cos(nx)dx
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Similar expressions
- (2/3(x+1))cos(nx)
Integral of (2/3(x-1))cos(nx) dx
The solution
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[src]
4 / | | 2*(x - 1) | ---------*cos(n*x) dx | 3 | / -4
$$\int\limits_{-4}^{4} \frac{2 \left(x - 1\right)}{3} \cos{\left(n x \right)}\, dx$$
Integral((2*(x - 1)/3)*cos(n*x), (x, -4, 4))
The answer (Indefinite)
[src]
// 2 \
|| x |
|| -- for n = 0|
|| 2 |
|| |
||/-cos(n*x) |
2*|<|---------- for n != 0 |
||< n |
// x for n = 0\ ||| | // x for n = 0\
|| | ||\ 0 otherwise | || |
/ 2*|
$$\int \frac{2 \left(x - 1\right)}{3} \cos{\left(n x \right)}\, dx = C + \frac{2 x \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(n x \right)}}{n} & \text{otherwise} \end{cases}\right)}{3} - \frac{2 \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(n x \right)}}{n} & \text{otherwise} \end{cases}\right)}{3} - \frac{2 \left(\begin{cases} \frac{x^{2}}{2} & \text{for}\: n = 0 \\\frac{\begin{cases} - \frac{\cos{\left(n x \right)}}{n} & \text{for}\: n \neq 0 \\0 & \text{otherwise} \end{cases}}{n} & \text{otherwise} \end{cases}\right)}{3}$$
The answer
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/-4*sin(4*n) |----------- for And(n > -oo, n < oo, n != 0) < 3*n | \ -16/3 otherwise
$$\begin{cases} - \frac{4 \sin{\left(4 n \right)}}{3 n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\- \frac{16}{3} & \text{otherwise} \end{cases}$$
=
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/-4*sin(4*n) |----------- for And(n > -oo, n < oo, n != 0) < 3*n | \ -16/3 otherwise
$$\begin{cases} - \frac{4 \sin{\left(4 n \right)}}{3 n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\- \frac{16}{3} & \text{otherwise} \end{cases}$$
Piecewise((-4*sin(4*n)/(3*n), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (-16/3, True))
Use the examples entering the upper and lower limits of integration.