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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
- Integral of x^2cosnx
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Integral of x^3-3x^2
- Integral of dx/(3cosx-4sinx+5)
- Integral of (sin(sqrt(x)+a)*e^sqrt(x))/sqrt(x)
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Identical expressions
- x^2cosnx
- x squared co sinus of e of nx
- x2cosnx
- x²cosnx
- x to the power of 2cosnx
- x^2cosnxdx
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Similar expressions
- (pi^2-x^2)*cos(n*x)
- x^2cos(nx)
Integral of x^2cosnx dx
The solution
You have entered
[src]
pi / | | 2 | x *cos(n*x) dx | / -pi
$$\int\limits_{- \pi}^{\pi} x^{2} \cos{\left(n x \right)}\, dx$$
Integral(x^2*cos(n*x), (x, -pi, pi))
The answer (Indefinite)
[src]
// 3 \
|| x |
|| -- for n = 0|
|| 3 |
/ || |
| ||/sin(n*x) x*cos(n*x) | // x for n = 0\
| 2 |||-------- - ---------- for n != 0 | 2 || |
| x *cos(n*x) dx = C - 2*|<| 2 n | + x *|
$${{\left(n^2\,x^2-2\right)\,\sin \left(n\,x\right)+2\,n\,x\,\cos
\left(n\,x\right)}\over{n^3}}$$
The answer
[src]
/ 2 | 4*sin(pi*n) 2*pi *sin(pi*n) 4*pi*cos(pi*n) |- ----------- + --------------- + -------------- for And(n > -oo, n < oo, n != 0) | 3 n 2 | n n < | 3 | 2*pi | ----- otherwise | 3 \
$${{2\,\left(\left(n^2\,\pi^2-2\right)\,\sin \left(n\,\pi\right)+2\,n
\,\pi\,\cos \left(n\,\pi\right)\right)}\over{n^3}}$$
=
=
/ 2 | 4*sin(pi*n) 2*pi *sin(pi*n) 4*pi*cos(pi*n) |- ----------- + --------------- + -------------- for And(n > -oo, n < oo, n != 0) | 3 n 2 | n n < | 3 | 2*pi | ----- otherwise | 3 \
$$\begin{cases} \frac{2 \pi^{2} \sin{\left(\pi n \right)}}{n} + \frac{4 \pi \cos{\left(\pi n \right)}}{n^{2}} - \frac{4 \sin{\left(\pi n \right)}}{n^{3}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{2 \pi^{3}}{3} & \text{otherwise} \end{cases}$$
Use the examples entering the upper and lower limits of integration.