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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*e^x*dx
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Integral of exp(x)/x
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Integral of x*exp(-x^2)
- Integral of x/(x-1)^2
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Identical expressions
- dx/(three + five *cos*x)
- dx divide by (3 plus 5 multiply by co sinus of e of multiply by x)
- dx divide by (three plus five multiply by co sinus of e of multiply by x)
- dx/(3+5cosx)
- dx/3+5cosx
- dx divide by (3+5*cos*x)
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Similar expressions
- dx/(3-5*cos*x)
Integral of dx/(3+5*cos*x) dx
The solution
You have entered
[src]
1 / | | 1 | ------------ dx | 3 + 5*cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{5 \cos{\left(x \right)} + 3}\, dx$$
Integral(1/(3 + 5*cos(x)), (x, 0, 1))
The answer (Indefinite)
[src]
/ / /x\\ / /x\\ | log|-2 + tan|-|| log|2 + tan|-|| | 1 \ \2// \ \2// | ------------ dx = C - ---------------- + --------------- | 3 + 5*cos(x) 4 4 | /
$$\int \frac{1}{5 \cos{\left(x \right)} + 3}\, dx = C - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 2 \right)}}{4} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 2 \right)}}{4}$$
The graph
The answer
[src]
log(2 - tan(1/2)) log(2 + tan(1/2))
- ----------------- + -----------------
4 4
$$- \frac{\log{\left(2 - \tan{\left(\frac{1}{2} \right)} \right)}}{4} + \frac{\log{\left(\tan{\left(\frac{1}{2} \right)} + 2 \right)}}{4}$$
=
=
log(2 - tan(1/2)) log(2 + tan(1/2))
- ----------------- + -----------------
4 4
$$- \frac{\log{\left(2 - \tan{\left(\frac{1}{2} \right)} \right)}}{4} + \frac{\log{\left(\tan{\left(\frac{1}{2} \right)} + 2 \right)}}{4}$$
-log(2 - tan(1/2))/4 + log(2 + tan(1/2))/4
Use the examples entering the upper and lower limits of integration.