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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x^3*ln(x)
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Integral of (1-cosx)/(1+cosx)
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Integral of x*dx/(x^2+1)
- Integral of tan^(-1)x
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Identical expressions
- (cosx)/(five +4cosx)
- ( co sinus of e of x) divide by (5 plus 4 co sinus of e of x)
- ( co sinus of e of x) divide by (five plus 4 co sinus of e of x)
- cosx/5+4cosx
- (cosx) divide by (5+4cosx)
- (cosx)/(5+4cosx)dx
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Similar expressions
- (cos(x))/(5+4*cos(x))
- cos(x)/(5+4cos(x))
- (cosx)/(5-4cosx)
Integral of (cosx)/(5+4cosx) dx
The solution
You have entered
[src]
n - 2 / | | cos(x) | ------------ dx | 5 + 4*cos(x) | / 0
$$\int\limits_{0}^{\frac{n}{2}} \frac{\cos{\left(x \right)}}{4 \cos{\left(x \right)} + 5}\, dx$$
Integral(cos(x)/(5 + 4*cos(x)), (x, 0, n/2))
The answer (Indefinite)
[src]
/ /x\\ /x pi\
|tan|-|| |- - --|
/ | \2/| |2 2 |
| 5*atan|------| 5*pi*floor|------|
| cos(x) \ 3 / x \ pi /
| ------------ dx = C - -------------- + - - ------------------
| 5 + 4*cos(x) 6 4 6
|
/
$$\int \frac{\cos{\left(x \right)}}{4 \cos{\left(x \right)} + 5}\, dx = C + \frac{x}{4} - \frac{5 \operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{3} \right)}}{6} - \frac{5 \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor}{6}$$
The answer
[src]
/ /n\\ / pi n\
|tan|-|| |- -- + -|
| \4/| | 2 4|
5*atan|------| 5*pi*floor|--------|
5*pi \ 3 / n \ pi /
- ---- - -------------- + - - --------------------
6 6 8 6
$$\frac{n}{8} - \frac{5 \operatorname{atan}{\left(\frac{\tan{\left(\frac{n}{4} \right)}}{3} \right)}}{6} - \frac{5 \pi \left\lfloor{\frac{\frac{n}{4} - \frac{\pi}{2}}{\pi}}\right\rfloor}{6} - \frac{5 \pi}{6}$$
=
=
/ /n\\ / pi n\
|tan|-|| |- -- + -|
| \4/| | 2 4|
5*atan|------| 5*pi*floor|--------|
5*pi \ 3 / n \ pi /
- ---- - -------------- + - - --------------------
6 6 8 6
$$\frac{n}{8} - \frac{5 \operatorname{atan}{\left(\frac{\tan{\left(\frac{n}{4} \right)}}{3} \right)}}{6} - \frac{5 \pi \left\lfloor{\frac{\frac{n}{4} - \frac{\pi}{2}}{\pi}}\right\rfloor}{6} - \frac{5 \pi}{6}$$
-5*pi/6 - 5*atan(tan(n/4)/3)/6 + n/8 - 5*pi*floor((-pi/2 + n/4)/pi)/6
Use the examples entering the upper and lower limits of integration.