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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(4+x^2)
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Integral of 1/(x^2+4x+8)
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Integral of (1+cos^2x)/(1+cos2x)
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Integral of 1/((x+1)(x^2+1))
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Identical expressions
- (sinx)/(five +4sinx)
- ( sinus of x) divide by (5 plus 4 sinus of x)
- ( sinus of x) divide by (five plus 4 sinus of x)
- sinx/5+4sinx
- (sinx) divide by (5+4sinx)
- (sinx)/(5+4sinx)dx
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Similar expressions
- (sinx)/(5-4sinx)
Integral of (sinx)/(5+4sinx) dx
The solution
You have entered
[src]
pi -- 2 / | | sin(x) | ------------ dx | 5 + 4*sin(x) | / 0
$$\int\limits_{0}^{\frac{\pi}{2}} \frac{\sin{\left(x \right)}}{4 \sin{\left(x \right)} + 5}\, dx$$
Integral(sin(x)/(5 + 4*sin(x)), (x, 0, pi/2))
The answer (Indefinite)
[src]
/ /x\\ /x pi\
| 5*tan|-|| |- - --|
/ |4 \2/| |2 2 |
| 5*atan|- + --------| 5*pi*floor|------|
| sin(x) \3 3 / x \ pi /
| ------------ dx = C - -------------------- + - - ------------------
| 5 + 4*sin(x) 6 4 6
|
/
$$\int \frac{\sin{\left(x \right)}}{4 \sin{\left(x \right)} + 5}\, dx = C + \frac{x}{4} - \frac{5 \operatorname{atan}{\left(\frac{5 \tan{\left(\frac{x}{2} \right)}}{3} + \frac{4}{3} \right)}}{6} - \frac{5 \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor}{6}$$
The graph
The answer
[src]
5*atan(3) pi 5*atan(4/3)
- --------- + -- + -----------
6 8 6
$$- \frac{5 \operatorname{atan}{\left(3 \right)}}{6} + \frac{\pi}{8} + \frac{5 \operatorname{atan}{\left(\frac{4}{3} \right)}}{6}$$
=
=
5*atan(3) pi 5*atan(4/3)
- --------- + -- + -----------
6 8 6
$$- \frac{5 \operatorname{atan}{\left(3 \right)}}{6} + \frac{\pi}{8} + \frac{5 \operatorname{atan}{\left(\frac{4}{3} \right)}}{6}$$
The graph
Use the examples entering the upper and lower limits of integration.