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Solving integrals/ 1/(sin(4x)+3)

Integral of 1/(sin(4x)+3) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |  sin(4*x) + 3   
 |                 
/                  
0
$$\int\limits_{0}^{1} \frac{1}{\sin{\left(4 x \right)} + 3}\, dx$$ 
Integral(1/(sin(4*x) + 3), (x, 0, 1))
The answer (Indefinite) [src] 
                               /        /      pi\                                 \
                               |        |2*x - --|       /  ___       ___         \|
  /                        ___ |        |      2 |       |\/ 2    3*\/ 2 *tan(2*x)||
 |                       \/ 2 *|pi*floor|--------| + atan|----- + ----------------||
 |      1                      \        \   pi   /       \  4            4        //
 | ------------ dx = C + -----------------------------------------------------------
 | sin(4*x) + 3                                       8                             
 |                                                                                  
/
$$\int \frac{1}{\sin{\left(4 x \right)} + 3}\, dx = C + \frac{\sqrt{2} \left(\operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(2 x \right)}}{4} + \frac{\sqrt{2}}{4} \right)} + \pi \left\lfloor{\frac{2 x - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{8}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
        /          /  ___\\             /  ___       ___       \
    ___ |          |\/ 2 ||     ___     |\/ 2    3*\/ 2 *tan(2)|
  \/ 2 *|-pi + atan|-----||   \/ 2 *atan|----- + --------------|
        \          \  4  //             \  4           4       /
- ------------------------- + ----------------------------------
              8                               8
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(2 \right)}}{4} + \frac{\sqrt{2}}{4} \right)}}{8} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right)}{8}$$ 
=
= 
        /          /  ___\\             /  ___       ___       \
    ___ |          |\/ 2 ||     ___     |\/ 2    3*\/ 2 *tan(2)|
  \/ 2 *|-pi + atan|-----||   \/ 2 *atan|----- + --------------|
        \          \  4  //             \  4           4       /
- ------------------------- + ----------------------------------
              8                               8
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(2 \right)}}{4} + \frac{\sqrt{2}}{4} \right)}}{8} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right)}{8}$$ 
-sqrt(2)*(-pi + atan(sqrt(2)/4))/8 + sqrt(2)*atan(sqrt(2)/4 + 3*sqrt(2)*tan(2)/4)/8
Numerical answer [src] 
0.30085725364222
0.30085725364222

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

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