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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^e
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Integral of e^(-x)*sin(2*x)
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Integral of 4*x^3
- Integral of ln(cosx)
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Identical expressions
- sin(x)/(five +3sin(x))
- sinus of (x) divide by (5 plus 3 sinus of (x))
- sinus of (x) divide by (five plus 3 sinus of (x))
- sinx/5+3sinx
- sin(x) divide by (5+3sin(x))
- sin(x)/(5+3sin(x))dx
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Similar expressions
- sin(x)/(5-3sin(x))
- sinx/(5+3sinx)
Integral of sin(x)/(5+3sin(x)) dx
The solution
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[src]
1 / | | sin(x) | ------------ dx | 5 + 3*sin(x) | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{3 \sin{\left(x \right)} + 5}\, dx$$
Integral(sin(x)/(5 + 3*sin(x)), (x, 0, 1))
The answer (Indefinite)
[src]
/ /x\\ /x pi\
| 5*tan|-|| |- - --|
/ |3 \2/| |2 2 |
| 5*atan|- + --------| 5*pi*floor|------|
| sin(x) \4 4 / x \ pi /
| ------------ dx = C - -------------------- + - - ------------------
| 5 + 3*sin(x) 6 3 6
|
/
$$\int \frac{\sin{\left(x \right)}}{3 \sin{\left(x \right)} + 5}\, dx = C + \frac{x}{3} - \frac{5 \operatorname{atan}{\left(\frac{5 \tan{\left(\frac{x}{2} \right)}}{4} + \frac{3}{4} \right)}}{6} - \frac{5 \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor}{6}$$
The graph
The answer
[src]
/3 5*tan(1/2)\
5*atan|- + ----------|
1 \4 4 / 5*atan(3/4)
- - ---------------------- + -----------
3 6 6
$$- \frac{5 \operatorname{atan}{\left(\frac{5 \tan{\left(\frac{1}{2} \right)}}{4} + \frac{3}{4} \right)}}{6} + \frac{1}{3} + \frac{5 \operatorname{atan}{\left(\frac{3}{4} \right)}}{6}$$
=
=
/3 5*tan(1/2)\
5*atan|- + ----------|
1 \4 4 / 5*atan(3/4)
- - ---------------------- + -----------
3 6 6
$$- \frac{5 \operatorname{atan}{\left(\frac{5 \tan{\left(\frac{1}{2} \right)}}{4} + \frac{3}{4} \right)}}{6} + \frac{1}{3} + \frac{5 \operatorname{atan}{\left(\frac{3}{4} \right)}}{6}$$
1/3 - 5*atan(3/4 + 5*tan(1/2)/4)/6 + 5*atan(3/4)/6
The graph
Use the examples entering the upper and lower limits of integration.