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Solving integrals/ 1/(4cos(x)-3sinx)

Integral 1/(4cos(x)-3sinx) dx

Limits of integration:

from to
v

Gráfico:

from to

Piecewise:

A solução

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       
 |                                                                 
/
$$\int \frac{1}{- 3 \sin{\left(x \right)} + 4 \cos{\left(x \right)}}\, dx = C - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{1}{2} \right)}}{5} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 2 \right)}}{5}$$
Simplify
The graph
Plot the graph f(x)
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
Numerical answer [src] 
0.711225308749378
0.711225308749378

    Use the examples entering the upper and lower limits of integration.

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