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- Integral of d{x}:
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Integral of 1/(x+2)^2
- Integral of e^(x/y)
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Integral of 7
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Integral of e^(x^3)
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Identical expressions
- (one)/(sin3x+ five)
- (1) divide by ( sinus of 3x plus 5)
- (one) divide by ( sinus of 3x plus five)
- 1/sin3x+5
- (1) divide by (sin3x+5)
- (1)/(sin3x+5)dx
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Similar expressions
- (1)/(sin3x-5)
Integral of (1)/(sin3x+5) dx
The solution
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[src]
1 / | | 1 | ------------ dx | sin(3*x) + 5 | / 0
$$\int\limits_{0}^{1} \frac{1}{\sin{\left(3 x \right)} + 5}\, dx$$
Integral(1/(sin(3*x) + 5), (x, 0, 1))
The answer (Indefinite)
[src]
/ / pi 3*x\ / ___ /3*x\\\
| |- -- + ---| | ___ 5*\/ 6 *tan|---|||
/ ___ | | 2 2 | |\/ 6 \ 2 /||
| \/ 6 *|pi*floor|----------| + atan|----- + ----------------||
| 1 \ \ pi / \ 12 12 //
| ------------ dx = C + -------------------------------------------------------------
| sin(3*x) + 5 18
|
/
$$\int \frac{1}{\sin{\left(3 x \right)} + 5}\, dx = C + \frac{\sqrt{6} \left(\operatorname{atan}{\left(\frac{5 \sqrt{6} \tan{\left(\frac{3 x}{2} \right)}}{12} + \frac{\sqrt{6}}{12} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{18}$$
The graph
The answer
[src]
/ / ___\\ / / ___ ___ \\
___ | |\/ 6 || ___ | |\/ 6 5*\/ 6 *tan(3/2)||
\/ 6 *|-pi + atan|-----|| \/ 6 *|-pi + atan|----- + ----------------||
\ \ 12 // \ \ 12 12 //
- ------------------------- + --------------------------------------------
18 18
$$\frac{\sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6}}{12} + \frac{5 \sqrt{6} \tan{\left(\frac{3}{2} \right)}}{12} \right)}\right)}{18} - \frac{\sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6}}{12} \right)}\right)}{18}$$
=
=
/ / ___\\ / / ___ ___ \\
___ | |\/ 6 || ___ | |\/ 6 5*\/ 6 *tan(3/2)||
\/ 6 *|-pi + atan|-----|| \/ 6 *|-pi + atan|----- + ----------------||
\ \ 12 // \ \ 12 12 //
- ------------------------- + --------------------------------------------
18 18
$$\frac{\sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6}}{12} + \frac{5 \sqrt{6} \tan{\left(\frac{3}{2} \right)}}{12} \right)}\right)}{18} - \frac{\sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6}}{12} \right)}\right)}{18}$$
-sqrt(6)*(-pi + atan(sqrt(6)/12))/18 + sqrt(6)*(-pi + atan(sqrt(6)/12 + 5*sqrt(6)*tan(3/2)/12))/18
Use the examples entering the upper and lower limits of integration.