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1/(4sinx+3cosx)
Solving integrals/ 1/(4sinx+3cosx)

Integral of 1/(4sinx+3cosx) dx

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The solution

You have entered [src] 
  1                       
  /                       
 |                        
 |           1            
 |  ------------------- dx
 |  4*sin(x) + 3*cos(x)   
 |                        
/                         
0
∫0114sin⁡(x)+3cos⁡(x) dx\int\limits_{0}^{1} \frac{1}{4 \sin{\left(x \right)} + 3 \cos{\left(x \right)}}\, dx 
Integral(1/(4*sin(x) + 3*cos(x)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                /        /x\\      /1      /x\\
 |                              log|-3 + tan|-||   log|- + tan|-||
 |          1                      \        \2//      \3      \2//
 | ------------------- dx = C - ---------------- + ---------------
 | 4*sin(x) + 3*cos(x)                 5                  5       
 |                                                                
/
∫14sin⁡(x)+3cos⁡(x) dx=C−log⁡(tan⁡(x2)−3)5+log⁡(tan⁡(x2)+13)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)} - 3 \right)}}{5} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{1}{3} \right)}}{5}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.10.4
Plot the graph f(x)
The answer [src] 
  log(3 - tan(1/2))   log(1/3 + tan(1/2))   2*log(3)
- ----------------- + ------------------- + --------
          5                    5               5
−log⁡(3−tan⁡(12))5+log⁡(13+tan⁡(12))5+2log⁡(3)5- \frac{\log{\left(3 - \tan{\left(\frac{1}{2} \right)} \right)}}{5} + \frac{\log{\left(\frac{1}{3} + \tan{\left(\frac{1}{2} \right)} \right)}}{5} + \frac{2 \log{\left(3 \right)}}{5} 
=
= 
  log(3 - tan(1/2))   log(1/3 + tan(1/2))   2*log(3)
- ----------------- + ------------------- + --------
          5                    5               5
−log⁡(3−tan⁡(12))5+log⁡(13+tan⁡(12))5+2log⁡(3)5- \frac{\log{\left(3 - \tan{\left(\frac{1}{2} \right)} \right)}}{5} + \frac{\log{\left(\frac{1}{3} + \tan{\left(\frac{1}{2} \right)} \right)}}{5} + \frac{2 \log{\left(3 \right)}}{5} 
-log(3 - tan(1/2))/5 + log(1/3 + tan(1/2))/5 + 2*log(3)/5
Numerical answer [src] 
0.234276241635452
0.234276241635452
The graph
Integral of 1/(4sinx+3cosx) dx

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

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