Mister Exam
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- Improper integral
- Double Integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(2+x^2)
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Integral of x*sin2x
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Integral of y^(-2/3)
- Integral of x/(x^3-3x+2)
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Identical expressions
- (sinxdx)/(two +sinx)
- ( sinus of xdx) divide by (2 plus sinus of x)
- ( sinus of xdx) divide by (two plus sinus of x)
- sinxdx/2+sinx
- (sinxdx) divide by (2+sinx)
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Similar expressions
- (sinxdx)/(2-sinx)
- sin(x)*dx/(2+sin(x))
Integral of (sinxdx)/(2+sinx) dx
The solution
You have entered
[src]
pi -- 2 / | | sin(x) | ---------- dx | 2 + sin(x) | / 0
$$\int\limits_{0}^{\frac{\pi}{2}} \frac{\sin{\left(x \right)}}{\sin{\left(x \right)} + 2}\, dx$$
Integral(sin(x)/(2 + sin(x)), (x, 0, pi/2))
The answer (Indefinite)
[src]
/ /x pi\ / ___ /x\\\
| |- - --| | ___ 2*\/ 3 *tan|-|||
/ ___ | |2 2 | |\/ 3 \2/||
| 4*\/ 3 *|pi*floor|------| + atan|----- + --------------||
| sin(x) \ \ pi / \ 3 3 //
| ---------- dx = C + x - ---------------------------------------------------------
| 2 + sin(x) 3
|
/
$$\int \frac{\sin{\left(x \right)}}{\sin{\left(x \right)} + 2}\, dx = C + x - \frac{4 \sqrt{3} \left(\operatorname{atan}{\left(\frac{2 \sqrt{3} \tan{\left(\frac{x}{2} \right)}}{3} + \frac{\sqrt{3}}{3} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{3}$$
The graph
The answer
[src]
___ pi 2*pi*\/ 3 -- - ---------- 2 9
$$- \frac{2 \sqrt{3} \pi}{9} + \frac{\pi}{2}$$
=
=
___ pi 2*pi*\/ 3 -- - ---------- 2 9
$$- \frac{2 \sqrt{3} \pi}{9} + \frac{\pi}{2}$$
pi/2 - 2*pi*sqrt(3)/9
Use the examples entering the upper and lower limits of integration.