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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
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How to use it?
- Integral of d{x}:
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Integral of sin(5x)cos(x)
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Integral of dx/(7-x^2)
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Integral of dx/(5+4cosx)
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Integral of dx/(5-12*x-9*x^2)
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Identical expressions
- dx/(five +4cosx)
- dx divide by (5 plus 4 co sinus of e of x)
- dx divide by (five plus 4 co sinus of e of x)
- dx/5+4cosx
- dx divide by (5+4cosx)
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Similar expressions
- dx/(5-4cosx)
- cos(x)dx/(5+4*cos(x))
Integral of dx/(5+4cosx) dx
The solution
You have entered
[src]
1 / | | 1 | ------------ dx | 5 + 4*cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{4 \cos{\left(x \right)} + 5}\, dx$$
Integral(1/(5 + 4*cos(x)), (x, 0, 1))
The answer (Indefinite)
[src]
/ /x\\ /x pi\
|tan|-|| |- - --|
/ | \2/| |2 2 |
| 2*atan|------| 2*pi*floor|------|
| 1 \ 3 / \ pi /
| ------------ dx = C + -------------- + ------------------
| 5 + 4*cos(x) 3 3
|
/
$$\int \frac{1}{4 \cos{\left(x \right)} + 5}\, dx = C + \frac{2 \operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{3} \right)}}{3} + \frac{2 \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor}{3}$$
The graph
The answer
[src]
/tan(1/2)\
2*atan|--------|
\ 3 /
----------------
3
$$\frac{2 \operatorname{atan}{\left(\frac{\tan{\left(\frac{1}{2} \right)}}{3} \right)}}{3}$$
=
=
/tan(1/2)\
2*atan|--------|
\ 3 /
----------------
3
$$\frac{2 \operatorname{atan}{\left(\frac{\tan{\left(\frac{1}{2} \right)}}{3} \right)}}{3}$$
2*atan(tan(1/2)/3)/3
The graph
Use the examples entering the upper and lower limits of integration.