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How to use it?
- Integral of d{x}:
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Integral of 4x²
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Integral of 4*x/(1+x^2)
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Integral of (1-sin(x))/(x+cos(x))
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Integral of 1/(sin^2x*cos^2x)
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Identical expressions
- sin(x)/(five +sin(x))
- sinus of (x) divide by (5 plus sinus of (x))
- sinus of (x) divide by (five plus sinus of (x))
- sinx/5+sinx
- sin(x) divide by (5+sin(x))
- sin(x)/(5+sin(x))dx
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Similar expressions
- sin(x)/(5-sin(x))
- sinx/(5+sinx)
Integral of sin(x)/(5+sin(x)) dx
The solution
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[src]
1 / | | sin(x) | ---------- dx | 5 + sin(x) | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\sin{\left(x \right)} + 5}\, dx$$
Integral(sin(x)/(5 + sin(x)), (x, 0, 1))
The answer (Indefinite)
[src]
/ /x pi\ / ___ /x\\\
| |- - --| | ___ 5*\/ 6 *tan|-|||
/ ___ | |2 2 | |\/ 6 \2/||
| 5*\/ 6 *|pi*floor|------| + atan|----- + --------------||
| sin(x) \ \ pi / \ 12 12 //
| ---------- dx = C + x - ---------------------------------------------------------
| 5 + sin(x) 6
|
/
$$\int \frac{\sin{\left(x \right)}}{\sin{\left(x \right)} + 5}\, dx = C + x - \frac{5 \sqrt{6} \left(\operatorname{atan}{\left(\frac{5 \sqrt{6} \tan{\left(\frac{x}{2} \right)}}{12} + \frac{\sqrt{6}}{12} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{6}$$
The graph
The answer
[src]
/ / ___ ___ \\ / / ___\\
___ | |\/ 6 5*\/ 6 *tan(1/2)|| ___ | |\/ 6 ||
5*\/ 6 *|-pi + atan|----- + ----------------|| 5*\/ 6 *|-pi + atan|-----||
\ \ 12 12 // \ \ 12 //
1 - ---------------------------------------------- + ---------------------------
6 6
$$\frac{5 \sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6}}{12} \right)}\right)}{6} + 1 - \frac{5 \sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6}}{12} + \frac{5 \sqrt{6} \tan{\left(\frac{1}{2} \right)}}{12} \right)}\right)}{6}$$
=
=
/ / ___ ___ \\ / / ___\\
___ | |\/ 6 5*\/ 6 *tan(1/2)|| ___ | |\/ 6 ||
5*\/ 6 *|-pi + atan|----- + ----------------|| 5*\/ 6 *|-pi + atan|-----||
\ \ 12 12 // \ \ 12 //
1 - ---------------------------------------------- + ---------------------------
6 6
$$\frac{5 \sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6}}{12} \right)}\right)}{6} + 1 - \frac{5 \sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6}}{12} + \frac{5 \sqrt{6} \tan{\left(\frac{1}{2} \right)}}{12} \right)}\right)}{6}$$
1 - 5*sqrt(6)*(-pi + atan(sqrt(6)/12 + 5*sqrt(6)*tan(1/2)/12))/6 + 5*sqrt(6)*(-pi + atan(sqrt(6)/12))/6
Use the examples entering the upper and lower limits of integration.