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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
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How to use it?
- Integral of d{x}:
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Integral of cos^4xdx
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Integral of sinx^2dx
- Integral of ln(sin(x))/sqrt(x)
- Integral of 1/(4cos(x)-3sinx)
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Identical expressions
- one /(4cos(x)-3sinx)
- 1 divide by (4 co sinus of e of (x) minus 3 sinus of x)
- one divide by (4 co sinus of e of (x) minus 3 sinus of x)
- 1/4cosx-3sinx
- 1 divide by (4cos(x)-3sinx)
- 1/(4cos(x)-3sinx)dx
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Similar expressions
- 1/(4cos(x)+3sinx)
- 1/4cos(x)-3sin(x)-6
- 1/(4cosx-3sinx)
Integral of 1/(4cos(x)-3sinx) dx
The solution
You have entered
[src]
1 / | | 1 | ------------------- dx | 4*cos(x) - 3*sin(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{- 3 \sin{\left(x \right)} + 4 \cos{\left(x \right)}}\, dx$$
Integral(1/(4*cos(x) - 3*sin(x)), (x, 0, 1))
The answer (Indefinite)
[src]
/ / 1 /x\\ / /x\\ | log|- - + tan|-|| log|2 + tan|-|| | 1 \ 2 \2// \ \2// | ------------------- dx = C - ----------------- + --------------- | 4*cos(x) - 3*sin(x) 5 5 | /
$$\int \frac{1}{- 3 \sin{\left(x \right)} + 4 \cos{\left(x \right)}}\, dx = C - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{1}{2} \right)}}{5} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 2 \right)}}{5}$$
The graph
The answer
[src]
2*log(2) log(-1/2 + tan(1/2)) log(2 + tan(1/2)) pi*I
- -------- - -------------------- + ----------------- + ----
5 5 5 5
$$- \frac{2 \log{\left(2 \right)}}{5} + \frac{\log{\left(\tan{\left(\frac{1}{2} \right)} + 2 \right)}}{5} - \frac{\log{\left(- \frac{1}{2} + \tan{\left(\frac{1}{2} \right)} \right)}}{5} + \frac{i \pi}{5}$$
=
=
2*log(2) log(-1/2 + tan(1/2)) log(2 + tan(1/2)) pi*I
- -------- - -------------------- + ----------------- + ----
5 5 5 5
$$- \frac{2 \log{\left(2 \right)}}{5} + \frac{\log{\left(\tan{\left(\frac{1}{2} \right)} + 2 \right)}}{5} - \frac{\log{\left(- \frac{1}{2} + \tan{\left(\frac{1}{2} \right)} \right)}}{5} + \frac{i \pi}{5}$$
-2*log(2)/5 - log(-1/2 + tan(1/2))/5 + log(2 + tan(1/2))/5 + pi*i/5
Use the examples entering the upper and lower limits of integration.