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Solving integrals/ senx/(3senx+4cosx)

Integral of senx/(3senx+4cosx) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                       
  /                       
 |                        
 |         sin(x)         
 |  ------------------- dx
 |  3*sin(x) + 4*cos(x)   
 |                        
/                         
0
∫01sin⁡(x)3sin⁡(x)+4cos⁡(x) dx\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{3 \sin{\left(x \right)} + 4 \cos{\left(x \right)}}\, dx 
Integral(sin(x)/(3*sin(x) + 4*cos(x)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                             
 |                                                              
 |        sin(x)                4*log(3*sin(x) + 4*cos(x))   3*x
 | ------------------- dx = C - -------------------------- + ---
 | 3*sin(x) + 4*cos(x)                      25                25
 |                                                              
/
∫sin⁡(x)3sin⁡(x)+4cos⁡(x) dx=C+3x25−4log⁡(3sin⁡(x)+4cos⁡(x))25\int \frac{\sin{\left(x \right)}}{3 \sin{\left(x \right)} + 4 \cos{\left(x \right)}}\, dx = C + \frac{3 x}{25} - \frac{4 \log{\left(3 \sin{\left(x \right)} + 4 \cos{\left(x \right)} \right)}}{25}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.5-0.5
Plot the graph f(x)
The answer [src] 
3    4*log(3*sin(1) + 4*cos(1))   4*log(4)
-- - -------------------------- + --------
25               25                  25
−4log⁡(4cos⁡(1)+3sin⁡(1))25+325+4log⁡(4)25- \frac{4 \log{\left(4 \cos{\left(1 \right)} + 3 \sin{\left(1 \right)} \right)}}{25} + \frac{3}{25} + \frac{4 \log{\left(4 \right)}}{25} 
=
= 
3    4*log(3*sin(1) + 4*cos(1))   4*log(4)
-- - -------------------------- + --------
25               25                  25
−4log⁡(4cos⁡(1)+3sin⁡(1))25+325+4log⁡(4)25- \frac{4 \log{\left(4 \cos{\left(1 \right)} + 3 \sin{\left(1 \right)} \right)}}{25} + \frac{3}{25} + \frac{4 \log{\left(4 \right)}}{25} 
3/25 - 4*log(3*sin(1) + 4*cos(1))/25 + 4*log(4)/25
Numerical answer [src] 
0.0946873043415358
0.0946873043415358

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

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