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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^5/(x^2+1)
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Integral of cos(3x)dx
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Integral of (4-x^2)^0.5
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Integral of cot^5xdx
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Identical expressions
- Cos^ two (x-10p)
- Cos squared (x minus 10p)
- Cos to the power of two (x minus 10p)
- Cos2(x-10p)
- Cos2x-10p
- Cos²(x-10p)
- Cos to the power of 2(x-10p)
- Cos^2x-10p
- Cos^2(x-10p)dx
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Similar expressions
- Cos^2(x+10p)
Integral of Cos^2(x-10p) dx
The solution
You have entered
[src]
p -- 81 / | | 2 | cos (x - 10*p) dx | / -p --- 8
$$\int\limits_{- \frac{p}{8}}^{\frac{p}{81}} \cos^{2}{\left(- 10 p + x \right)}\, dx$$
Integral(cos(x - 10*p)^2, (x, -p/8, p/81))
The answer
[src]
/81*p\ /81*p\ /809*p\ /809*p\ 2/81*p\ 2/81*p\ 2/809*p\ 2/809*p\
cos|----|*sin|----| cos|-----|*sin|-----| p*cos |----| p*sin |----| p*cos |-----| p*sin |-----|
\ 8 / \ 8 / \ 81 / \ 81 / \ 8 / \ 8 / \ 81 / \ 81 /
------------------- - --------------------- + ------------ + ------------ + ------------- + -------------
2 2 16 16 162 162
$$\frac{p \sin^{2}{\left(\frac{809 p}{81} \right)}}{162} + \frac{p \sin^{2}{\left(\frac{81 p}{8} \right)}}{16} + \frac{p \cos^{2}{\left(\frac{809 p}{81} \right)}}{162} + \frac{p \cos^{2}{\left(\frac{81 p}{8} \right)}}{16} - \frac{\sin{\left(\frac{809 p}{81} \right)} \cos{\left(\frac{809 p}{81} \right)}}{2} + \frac{\sin{\left(\frac{81 p}{8} \right)} \cos{\left(\frac{81 p}{8} \right)}}{2}$$
=
=
/81*p\ /81*p\ /809*p\ /809*p\ 2/81*p\ 2/81*p\ 2/809*p\ 2/809*p\
cos|----|*sin|----| cos|-----|*sin|-----| p*cos |----| p*sin |----| p*cos |-----| p*sin |-----|
\ 8 / \ 8 / \ 81 / \ 81 / \ 8 / \ 8 / \ 81 / \ 81 /
------------------- - --------------------- + ------------ + ------------ + ------------- + -------------
2 2 16 16 162 162
$$\frac{p \sin^{2}{\left(\frac{809 p}{81} \right)}}{162} + \frac{p \sin^{2}{\left(\frac{81 p}{8} \right)}}{16} + \frac{p \cos^{2}{\left(\frac{809 p}{81} \right)}}{162} + \frac{p \cos^{2}{\left(\frac{81 p}{8} \right)}}{16} - \frac{\sin{\left(\frac{809 p}{81} \right)} \cos{\left(\frac{809 p}{81} \right)}}{2} + \frac{\sin{\left(\frac{81 p}{8} \right)} \cos{\left(\frac{81 p}{8} \right)}}{2}$$
cos(81*p/8)*sin(81*p/8)/2 - cos(809*p/81)*sin(809*p/81)/2 + p*cos(81*p/8)^2/16 + p*sin(81*p/8)^2/16 + p*cos(809*p/81)^2/162 + p*sin(809*p/81)^2/162
Use the examples entering the upper and lower limits of integration.