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How to use it?
- Integral of d{x}:
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Integral of x/x
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Integral of a
- Integral of e^(a*x)*sin(b*x)
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Integral of -1/t
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Identical expressions
- cos(x+pi/ eight)^ two
- co sinus of e of (x plus Pi divide by 8) squared
- co sinus of e of (x plus Pi divide by eight) to the power of two
- cos(x+pi/8)2
- cosx+pi/82
- cos(x+pi/8)²
- cos(x+pi/8) to the power of 2
- cosx+pi/8^2
- cos(x+pi divide by 8)^2
- cos(x+pi/8)^2dx
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Similar expressions
- cos(x-pi/8)^2
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What you mean?
- cos((x + pi)/8)^2
- cos(x + pi/8)^2
- cos(x + pi/8)^2
You entered:
cos(x+pi/8)^2
What you mean?
Integral of cos(x+pi/8)^2 dx
The solution
You have entered
[src]
pi -- 4 / | | 2/ pi\ | cos |x + --| dx | \ 8 / | / 0
$$\int\limits_{0}^{\frac{\pi}{4}} \cos^{2}{\left(x + \frac{\pi}{8} \right)}\, dx$$
Integral(cos(x + pi/8)^2, (x, 0, pi/4))
The answer (Indefinite)
[src]
/ 3/x pi\ /x pi\ 4/x pi\ 2/x pi\ | 2*tan |- + --| 2*tan|- + --| x*tan |- + --| 2*x*tan |- + --| | 2/ pi\ x \2 16/ \2 16/ \2 16/ \2 16/ | cos |x + --| dx = C + ----------------------------------- - ----------------------------------- + ----------------------------------- + ----------------------------------- + ----------------------------------- | \ 8 / 4/x pi\ 2/x pi\ 4/x pi\ 2/x pi\ 4/x pi\ 2/x pi\ 4/x pi\ 2/x pi\ 4/x pi\ 2/x pi\ | 2 + 2*tan |- + --| + 4*tan |- + --| 2 + 2*tan |- + --| + 4*tan |- + --| 2 + 2*tan |- + --| + 4*tan |- + --| 2 + 2*tan |- + --| + 4*tan |- + --| 2 + 2*tan |- + --| + 4*tan |- + --| / \2 16/ \2 16/ \2 16/ \2 16/ \2 16/ \2 16/ \2 16/ \2 16/ \2 16/ \2 16/
$$\int \cos^{2}{\left(x + \frac{\pi}{8} \right)}\, dx = C + \frac{x \tan^{4}{\left(\frac{x}{2} + \frac{\pi}{16} \right)}}{2 \tan^{4}{\left(\frac{x}{2} + \frac{\pi}{16} \right)} + 4 \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{16} \right)} + 2} + \frac{2 x \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{16} \right)}}{2 \tan^{4}{\left(\frac{x}{2} + \frac{\pi}{16} \right)} + 4 \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{16} \right)} + 2} + \frac{x}{2 \tan^{4}{\left(\frac{x}{2} + \frac{\pi}{16} \right)} + 4 \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{16} \right)} + 2} - \frac{2 \tan^{3}{\left(\frac{x}{2} + \frac{\pi}{16} \right)}}{2 \tan^{4}{\left(\frac{x}{2} + \frac{\pi}{16} \right)} + 4 \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{16} \right)} + 2} + \frac{2 \tan{\left(\frac{x}{2} + \frac{\pi}{16} \right)}}{2 \tan^{4}{\left(\frac{x}{2} + \frac{\pi}{16} \right)} + 4 \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{16} \right)} + 2}$$
The graph
The answer
[src]
/ ___\ / ___\
|1 \/ 2 | |1 \/ 2 |
pi*|- - -----| pi*|- + -----|
\2 4 / \2 4 /
-------------- + --------------
8 8
$$\frac{\pi \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)}{8} + \frac{\pi \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)}{8}$$
=
=
/ ___\ / ___\
|1 \/ 2 | |1 \/ 2 |
pi*|- - -----| pi*|- + -----|
\2 4 / \2 4 /
-------------- + --------------
8 8
$$\frac{\pi \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)}{8} + \frac{\pi \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)}{8}$$
pi*(1/2 - sqrt(2)/4)/8 + pi*(1/2 + sqrt(2)/4)/8
The graph
Use the examples entering the upper and lower limits of integration.