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