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- Improper integral
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How to use it?
- Integral of d{x}:
- Integral of (x+cosx)/(x^2+2sinx)
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Integral of sin(3x)*cos(7x)
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Integral of 2cosxdx
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Integral of sin^3x/1+cos^2x
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Identical expressions
- sin(x)*cos(nx)
- sinus of (x) multiply by co sinus of e of (nx)
- sin(x)cos(nx)
- sinxcosnx
- sin(x)*cos(nx)dx
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Similar expressions
- x*sin(x)cos(n*x)
- sin(x)*cos(n*x)
- sinxcosnx
- sinx*cos(nx)
Integral of sin(x)*cos(nx) dx
The solution
You have entered
[src]
0 / | | sin(x)*cos(n*x) dx | / -pi
$$\int\limits_{- \pi}^{0} \sin{\left(x \right)} \cos{\left(n x \right)}\, dx$$
Integral(sin(x)*cos(n*x), (x, -pi, 0))
The answer (Indefinite)
[src]
// 2 \
|| -cos (x) |
/ || --------- for Or(n = -1, n = 1)|
| || 2 |
| sin(x)*cos(n*x) dx = C + |< |
| ||cos(x)*cos(n*x) n*sin(x)*sin(n*x) |
/ ||--------------- + ----------------- otherwise |
|| 2 2 |
\\ -1 + n -1 + n /
$$-{{\cos \left(\left(n+1\right)\,x\right)}\over{2\,\left(n+1\right)
}}-{{\cos \left(\left(1-n\right)\,x\right)}\over{2\,\left(1-n\right)
}}$$
The answer
[src]
/ 0 for Or(n = -1, n = 1) | | 1 cos(pi*n) <------- + --------- otherwise | 2 2 |-1 + n -1 + n \
$${{\left(n-1\right)\,\cos \left(\left(n+1\right)\,\pi\right)+\left(-
n-1\right)\,\cos \left(\left(1-n\right)\,\pi\right)}\over{2\,n^2-2}}
+{{1}\over{n^2-1}}$$
=
=
/ 0 for Or(n = -1, n = 1) | | 1 cos(pi*n) <------- + --------- otherwise | 2 2 |-1 + n -1 + n \
$$\begin{cases} 0 & \text{for}\: n = -1 \vee n = 1 \\\frac{\cos{\left(\pi n \right)}}{n^{2} - 1} + \frac{1}{n^{2} - 1} & \text{otherwise} \end{cases}$$
Use the examples entering the upper and lower limits of integration.