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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of x*2^(-x)
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Integral of ex^2
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Integral of (1/x^2)dx
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Integral of x*cos(x/2)
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Identical expressions
- (dx)/(two *sin(x)+cos(x))
- (dx) divide by (2 multiply by sinus of (x) plus co sinus of e of (x))
- (dx) divide by (two multiply by sinus of (x) plus co sinus of e of (x))
- (dx)/(2sin(x)+cos(x))
- dx/2sinx+cosx
- (dx) divide by (2*sin(x)+cos(x))
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Similar expressions
- dx/2sinx+cosx
- (dx)/(2*sin(x)-cos(x))
- (dx)/(2*sinx+cosx)
Integral of (dx)/(2*sin(x)+cos(x)) dx
The solution
You have entered
[src]
1 / | | 1 | ----------------- dx | 2*sin(x) + cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{2 \sin{\left(x \right)} + \cos{\left(x \right)}}\, dx$$
Integral(1/(2*sin(x) + cos(x)), (x, 0, 1))
The graph
The answer
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___ / / ___ \\ ___ / ___\ ___ / / ___\\ ___ / ___ \
\/ 5 *\pi*I + log\2 + \/ 5 - tan(1/2)// \/ 5 *log\-2 + \/ 5 / \/ 5 *\pi*I + log\2 + \/ 5 // \/ 5 *log\-2 + \/ 5 + tan(1/2)/
- ---------------------------------------- - --------------------- + ----------------------------- + --------------------------------
5 5 5 5
$$\frac{\sqrt{5} \log{\left(-2 + \tan{\left(\frac{1}{2} \right)} + \sqrt{5} \right)}}{5} - \frac{\sqrt{5} \log{\left(-2 + \sqrt{5} \right)}}{5} - \frac{\sqrt{5} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 2 + \sqrt{5} \right)} + i \pi\right)}{5} + \frac{\sqrt{5} \left(\log{\left(2 + \sqrt{5} \right)} + i \pi\right)}{5}$$
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___ / / ___ \\ ___ / ___\ ___ / / ___\\ ___ / ___ \
\/ 5 *\pi*I + log\2 + \/ 5 - tan(1/2)// \/ 5 *log\-2 + \/ 5 / \/ 5 *\pi*I + log\2 + \/ 5 // \/ 5 *log\-2 + \/ 5 + tan(1/2)/
- ---------------------------------------- - --------------------- + ----------------------------- + --------------------------------
5 5 5 5
$$\frac{\sqrt{5} \log{\left(-2 + \tan{\left(\frac{1}{2} \right)} + \sqrt{5} \right)}}{5} - \frac{\sqrt{5} \log{\left(-2 + \sqrt{5} \right)}}{5} - \frac{\sqrt{5} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 2 + \sqrt{5} \right)} + i \pi\right)}{5} + \frac{\sqrt{5} \left(\log{\left(2 + \sqrt{5} \right)} + i \pi\right)}{5}$$
-sqrt(5)*(pi*i + log(2 + sqrt(5) - tan(1/2)))/5 - sqrt(5)*log(-2 + sqrt(5))/5 + sqrt(5)*(pi*i + log(2 + sqrt(5)))/5 + sqrt(5)*log(-2 + sqrt(5) + tan(1/2))/5
Use the examples entering the upper and lower limits of integration.