Mister Exam
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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^(4/5)
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Integral of (x^2)sinx
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Integral of 6x+3
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Integral of sin³xcosx
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Identical expressions
- (dx)/(three *cos(x)- four *sin(x))
- (dx) divide by (3 multiply by co sinus of e of (x) minus 4 multiply by sinus of (x))
- (dx) divide by (three multiply by co sinus of e of (x) minus four multiply by sinus of (x))
- (dx)/(3cos(x)-4sin(x))
- dx/3cosx-4sinx
- (dx) divide by (3*cos(x)-4*sin(x))
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Similar expressions
- (dx)/(3*cos(x)+4*sin(x))
- (dx)/(3*cosx-4*sinx)
Integral of (dx)/(3*cos(x)-4*sin(x)) dx
The solution
You have entered
[src]
1 / | | 1 | ------------------- dx | 3*cos(x) - 4*sin(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{- 4 \sin{\left(x \right)} + 3 \cos{\left(x \right)}}\, dx$$
Integral(1/(3*cos(x) - 4*sin(x)), (x, 0, 1))
The answer (Indefinite)
[src]
/ / 1 /x\\ / /x\\ | log|- - + tan|-|| log|3 + tan|-|| | 1 \ 3 \2// \ \2// | ------------------- dx = C - ----------------- + --------------- | 3*cos(x) - 4*sin(x) 5 5 | /
$$\int \frac{1}{- 4 \sin{\left(x \right)} + 3 \cos{\left(x \right)}}\, dx = C - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{1}{3} \right)}}{5} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 3 \right)}}{5}$$
The graph
The answer
[src]
2*log(3) log(-1/3 + tan(1/2)) log(3 + tan(1/2)) pi*I
- -------- - -------------------- + ----------------- + ----
5 5 5 5
$$- \frac{2 \log{\left(3 \right)}}{5} + \frac{\log{\left(\tan{\left(\frac{1}{2} \right)} + 3 \right)}}{5} - \frac{\log{\left(- \frac{1}{3} + \tan{\left(\frac{1}{2} \right)} \right)}}{5} + \frac{i \pi}{5}$$
=
=
2*log(3) log(-1/3 + tan(1/2)) log(3 + tan(1/2)) pi*I
- -------- - -------------------- + ----------------- + ----
5 5 5 5
$$- \frac{2 \log{\left(3 \right)}}{5} + \frac{\log{\left(\tan{\left(\frac{1}{2} \right)} + 3 \right)}}{5} - \frac{\log{\left(- \frac{1}{3} + \tan{\left(\frac{1}{2} \right)} \right)}}{5} + \frac{i \pi}{5}$$
-2*log(3)/5 - log(-1/3 + tan(1/2))/5 + log(3 + tan(1/2))/5 + pi*i/5
Use the examples entering the upper and lower limits of integration.