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×e^x
-
Integral of 1/(x²+1)
-
Integral of 1/√(1-4x^2)
-
Integral of f(x)=4x
-
Identical expressions
- one /(seven +5cosx)
- 1 divide by (7 plus 5 co sinus of e of x)
- one divide by (seven plus 5 co sinus of e of x)
- 1/7+5cosx
- 1 divide by (7+5cosx)
- 1/(7+5cosx)dx
-
Similar expressions
- 1/(7-5cosx)
Integral of 1/(7+5cosx) dx
The solution
You have entered
[src]
1 / | | 1 | ------------ dx | 7 + 5*cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{5 \cos{\left(x \right)} + 7}\, dx$$
Integral(1/(7 + 5*cos(x)), (x, 0, 1))
The answer (Indefinite)
[src]
/ /x pi\ / ___ /x\\\
| |- - --| |\/ 6 *tan|-|||
/ ___ | |2 2 | | \2/||
| \/ 6 *|pi*floor|------| + atan|------------||
| 1 \ \ pi / \ 6 //
| ------------ dx = C + ---------------------------------------------
| 7 + 5*cos(x) 6
|
/
$$\int \frac{1}{5 \cos{\left(x \right)} + 7}\, dx = C + \frac{\sqrt{6} \left(\operatorname{atan}{\left(\frac{\sqrt{6} \tan{\left(\frac{x}{2} \right)}}{6} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{6}$$
The graph
The answer
[src]
/ / ___ \\
___ | |\/ 6 *tan(1/2)||
___ \/ 6 *|-pi + atan|--------------||
pi*\/ 6 \ \ 6 //
-------- + ----------------------------------
6 6
$$\frac{\sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6} \tan{\left(\frac{1}{2} \right)}}{6} \right)}\right)}{6} + \frac{\sqrt{6} \pi}{6}$$
=
=
/ / ___ \\
___ | |\/ 6 *tan(1/2)||
___ \/ 6 *|-pi + atan|--------------||
pi*\/ 6 \ \ 6 //
-------- + ----------------------------------
6 6
$$\frac{\sqrt{6} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{6} \tan{\left(\frac{1}{2} \right)}}{6} \right)}\right)}{6} + \frac{\sqrt{6} \pi}{6}$$
pi*sqrt(6)/6 + sqrt(6)*(-pi + atan(sqrt(6)*tan(1/2)/6))/6
Use the examples entering the upper and lower limits of integration.