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- Improper integral
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How to use it?
- Integral of d{x}:
- Integral of cos(1-2x)dx
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Integral of tg²xdx
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Integral of sin^5(x)cos(x)dx
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Integral of cos(5x)cos(7x)
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Identical expressions
- e^(2x)*cos(nx)
- e to the power of (2x) multiply by co sinus of e of (nx)
- e(2x)*cos(nx)
- e2x*cosnx
- e^(2x)cos(nx)
- e(2x)cos(nx)
- e2xcosnx
- e^2xcosnx
- e^(2x)*cos(nx)dx
Integral of e^(2x)*cos(nx) dx
The solution
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[src]
pi / | | 2*x | E *cos(n*x) dx | / -pi
$$\int\limits_{- \pi}^{\pi} e^{2 x} \cos{\left(n x \right)}\, dx$$
Integral(E^(2*x)*cos(n*x), (x, -pi, pi))
The answer (Indefinite)
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/ | 2*x 2*x | 2*x 2*cos(n*x)*e n*e *sin(n*x) | E *cos(n*x) dx = C + --------------- + --------------- | 2 2 / 4 + n 4 + n
$$\int e^{2 x} \cos{\left(n x \right)}\, dx = C + \frac{n e^{2 x} \sin{\left(n x \right)}}{n^{2} + 4} + \frac{2 e^{2 x} \cos{\left(n x \right)}}{n^{2} + 4}$$
The answer
[src]
-2*pi 2*pi -2*pi 2*pi
2*cos(pi*n)*e 2*cos(pi*n)*e n*e *sin(pi*n) n*e *sin(pi*n)
- ------------------ + ----------------- + ------------------ + -----------------
2 2 2 2
4 + n 4 + n 4 + n 4 + n
$$\frac{n \sin{\left(\pi n \right)}}{\left(n^{2} + 4\right) e^{2 \pi}} + \frac{n e^{2 \pi} \sin{\left(\pi n \right)}}{n^{2} + 4} - \frac{2 \cos{\left(\pi n \right)}}{\left(n^{2} + 4\right) e^{2 \pi}} + \frac{2 e^{2 \pi} \cos{\left(\pi n \right)}}{n^{2} + 4}$$
=
=
-2*pi 2*pi -2*pi 2*pi
2*cos(pi*n)*e 2*cos(pi*n)*e n*e *sin(pi*n) n*e *sin(pi*n)
- ------------------ + ----------------- + ------------------ + -----------------
2 2 2 2
4 + n 4 + n 4 + n 4 + n
$$\frac{n \sin{\left(\pi n \right)}}{\left(n^{2} + 4\right) e^{2 \pi}} + \frac{n e^{2 \pi} \sin{\left(\pi n \right)}}{n^{2} + 4} - \frac{2 \cos{\left(\pi n \right)}}{\left(n^{2} + 4\right) e^{2 \pi}} + \frac{2 e^{2 \pi} \cos{\left(\pi n \right)}}{n^{2} + 4}$$
-2*cos(pi*n)*exp(-2*pi)/(4 + n^2) + 2*cos(pi*n)*exp(2*pi)/(4 + n^2) + n*exp(-2*pi)*sin(pi*n)/(4 + n^2) + n*exp(2*pi)*sin(pi*n)/(4 + n^2)
Use the examples entering the upper and lower limits of integration.