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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of cos2xsinx
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Integral of (-1)^x
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Integral of (x^3-1)/(x+3)
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Integral of x^2/(x^2-5*x+6)
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Identical expressions
- one /(cos(x)-sin(x))
- 1 divide by ( co sinus of e of (x) minus sinus of (x))
- one divide by ( co sinus of e of (x) minus sinus of (x))
- 1/cosx-sinx
- 1 divide by (cos(x)-sin(x))
- 1/(cos(x)-sin(x))dx
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Similar expressions
- 1/(cos(x)+sin(x))
- 1/(cosx-sinx)
Integral of 1/(cos(x)-sin(x)) dx
The solution
You have entered
[src]
pi -- 3 / | | 1 | --------------- dx | cos(x) - sin(x) | / 0
$$\int\limits_{0}^{\frac{\pi}{3}} \frac{1}{- \sin{\left(x \right)} + \cos{\left(x \right)}}\, dx$$
Integral(1/(cos(x) - sin(x)), (x, 0, pi/3))
The answer (Indefinite)
[src]
/ ___ / ___ /x\\ ___ / ___ /x\\ | \/ 2 *log|1 + \/ 2 + tan|-|| \/ 2 *log|1 - \/ 2 + tan|-|| | 1 \ \2// \ \2// | --------------- dx = C + ----------------------------- - ----------------------------- | cos(x) - sin(x) 2 2 | /
$$\int \frac{1}{- \sin{\left(x \right)} + \cos{\left(x \right)}}\, dx = C + \frac{\sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{2} - \frac{\sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{2}$$
The graph
Use the examples entering the upper and lower limits of integration.