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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(2+x^2)
- Integral of x/(x^3-3x+2)
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Integral of -x+4
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Integral of 8/x^2
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Identical expressions
- one /(sin(x+pi/ three)^ two)
- 1 divide by ( sinus of (x plus Pi divide by 3) squared )
- one divide by ( sinus of (x plus Pi divide by three) to the power of two)
- 1/(sin(x+pi/3)2)
- 1/sinx+pi/32
- 1/(sin(x+pi/3)²)
- 1/(sin(x+pi/3) to the power of 2)
- 1/sinx+pi/3^2
- 1 divide by (sin(x+pi divide by 3)^2)
- 1/(sin(x+pi/3)^2)dx
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Similar expressions
- 1/(sin(x-pi/3)^2)
Integral of 1/(sin(x+pi/3)^2) dx
The solution
You have entered
[src]
pi -- 6 / | | 1 | ------------ dx | 2/ pi\ | sin |x + --| | \ 3 / | / 0
$$\int\limits_{0}^{\frac{\pi}{6}} \frac{1}{\sin^{2}{\left(x + \frac{\pi}{3} \right)}}\, dx$$
Integral(1/(sin(x + pi/3)^2), (x, 0, pi/6))
The answer (Indefinite)
[src]
/ /x pi\ | tan|- + --| | 1 \2 6 / 1 | ------------ dx = C + ----------- - ------------- | 2/ pi\ 2 /x pi\ | sin |x + --| 2*tan|- + --| | \ 3 / \2 6 / | /
$$\int \frac{1}{\sin^{2}{\left(x + \frac{\pi}{3} \right)}}\, dx = C + \frac{\tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}{2} - \frac{1}{2 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}$$
The graph
The answer
[src]
___ \/ 3 ----- 3
$$\frac{\sqrt{3}}{3}$$
=
=
___ \/ 3 ----- 3
$$\frac{\sqrt{3}}{3}$$
sqrt(3)/3
Use the examples entering the upper and lower limits of integration.