Mister Exam
Other calculators
- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Integral of d{x}:
-
Integral of x^2*e^x
-
Integral of √xdx
-
Integral of √(1-x^2)
-
Integral of 1/(2x)
-
Identical expressions
- one /(sin3x+ six)
- 1 divide by ( sinus of 3x plus 6)
- one divide by ( sinus of 3x plus six)
- 1/sin3x+6
- 1 divide by (sin3x+6)
- 1/(sin3x+6)dx
-
Similar expressions
- 1/(sin3x-6)
Integral of 1/(sin3x+6) dx
The solution
You have entered
[src]
1 / | | 1 | ------------ dx | sin(3*x) + 6 | / 0
$$\int\limits_{0}^{1} \frac{1}{\sin{\left(3 x \right)} + 6}\, dx$$
Integral(1/(sin(3*x) + 6), (x, 0, 1))
The answer (Indefinite)
[src]
/ / pi 3*x\ / ____ /3*x\\\
| |- -- + ---| | ____ 6*\/ 35 *tan|---|||
/ ____ | | 2 2 | |\/ 35 \ 2 /||
| 2*\/ 35 *|pi*floor|----------| + atan|------ + -----------------||
| 1 \ \ pi / \ 35 35 //
| ------------ dx = C + ------------------------------------------------------------------
| sin(3*x) + 6 105
|
/
$$\int \frac{1}{\sin{\left(3 x \right)} + 6}\, dx = C + \frac{2 \sqrt{35} \left(\operatorname{atan}{\left(\frac{6 \sqrt{35} \tan{\left(\frac{3 x}{2} \right)}}{35} + \frac{\sqrt{35}}{35} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{105}$$
The graph
The answer
[src]
/ / ____\\ / / ____ ____ \\
____ | |\/ 35 || ____ | |\/ 35 6*\/ 35 *tan(3/2)||
2*\/ 35 *|-pi + atan|------|| 2*\/ 35 *|-pi + atan|------ + -----------------||
\ \ 35 // \ \ 35 35 //
- ----------------------------- + -------------------------------------------------
105 105
$$\frac{2 \sqrt{35} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{35}}{35} + \frac{6 \sqrt{35} \tan{\left(\frac{3}{2} \right)}}{35} \right)}\right)}{105} - \frac{2 \sqrt{35} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{35}}{35} \right)}\right)}{105}$$
=
=
/ / ____\\ / / ____ ____ \\
____ | |\/ 35 || ____ | |\/ 35 6*\/ 35 *tan(3/2)||
2*\/ 35 *|-pi + atan|------|| 2*\/ 35 *|-pi + atan|------ + -----------------||
\ \ 35 // \ \ 35 35 //
- ----------------------------- + -------------------------------------------------
105 105
$$\frac{2 \sqrt{35} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{35}}{35} + \frac{6 \sqrt{35} \tan{\left(\frac{3}{2} \right)}}{35} \right)}\right)}{105} - \frac{2 \sqrt{35} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{35}}{35} \right)}\right)}{105}$$
-2*sqrt(35)*(-pi + atan(sqrt(35)/35))/105 + 2*sqrt(35)*(-pi + atan(sqrt(35)/35 + 6*sqrt(35)*tan(3/2)/35))/105
Use the examples entering the upper and lower limits of integration.