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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x^4*e^(2*x)*dx
- Integral of x/(x^2-3x+2)
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Integral of x^-3dx
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Integral of (x^2+x)dx
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Identical expressions
- (sin8xcos2x)/ four
- ( sinus of 8x co sinus of e of 2x) divide by 4
- ( sinus of 8x co sinus of e of 2x) divide by four
- sin8xcos2x/4
- (sin8xcos2x) divide by 4
- (sin8xcos2x)/4dx
Integral of (sin8xcos2x)/4 dx
The solution
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[src]
pi -- 61 / | | sin(8*x)*cos(2*x) | ----------------- dx | 4 | / 0
$$\int\limits_{0}^{\frac{\pi}{61}} \frac{\sin{\left(8 x \right)} \cos{\left(2 x \right)}}{4}\, dx$$
Integral((sin(8*x)*cos(2*x))/4, (x, 0, pi/61))
The graph
The answer
[src]
/2*pi\ /8*pi\ /2*pi\ /8*pi\
cos|----|*cos|----| sin|----|*sin|----|
1 \ 61 / \ 61 / \ 61 / \ 61 /
-- - ------------------- - -------------------
30 30 120
$$- \frac{\cos{\left(\frac{2 \pi}{61} \right)} \cos{\left(\frac{8 \pi}{61} \right)}}{30} - \frac{\sin{\left(\frac{2 \pi}{61} \right)} \sin{\left(\frac{8 \pi}{61} \right)}}{120} + \frac{1}{30}$$
=
=
/2*pi\ /8*pi\ /2*pi\ /8*pi\
cos|----|*cos|----| sin|----|*sin|----|
1 \ 61 / \ 61 / \ 61 / \ 61 /
-- - ------------------- - -------------------
30 30 120
$$- \frac{\cos{\left(\frac{2 \pi}{61} \right)} \cos{\left(\frac{8 \pi}{61} \right)}}{30} - \frac{\sin{\left(\frac{2 \pi}{61} \right)} \sin{\left(\frac{8 \pi}{61} \right)}}{120} + \frac{1}{30}$$
1/30 - cos(2*pi/61)*cos(8*pi/61)/30 - sin(2*pi/61)*sin(8*pi/61)/120
Use the examples entering the upper and lower limits of integration.