Mister Exam

Other calculators

  • How to use it?

  • Integral of d{x}:
  • Integral of sin(5x) Integral of sin(5x)
  • Integral of 0dx Integral of 0dx
  • Integral of -x+4 Integral of -x+4
  • Integral of (x-2)^2dx Integral of (x-2)^2dx

  • Identical expressions

  • one /(sin(x+pi/ three)^ two)
  • 1 divide by ( sinus of (x plus Pi divide by 3) squared )
  • one divide by ( sinus of (x plus Pi divide by three) to the power of two)
  • 1/(sin(x+pi/3)2)
  • 1/sinx+pi/32
  • 1/(sin(x+pi/3)²)
  • 1/(sin(x+pi/3) to the power of 2)
  • 1/sinx+pi/3^2
  • 1 divide by (sin(x+pi divide by 3)^2)
  • 1/(sin(x+pi/3)^2)dx

  • Similar expressions

  • 1/(sin(x-pi/3)^2)
Solving integrals/ 1/(sin(x+pi/3)^2)

Integral of 1/(sin(x+pi/3)^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                
 --                
 6                 
  /                
 |                 
 |       1         
 |  ------------ dx
 |     2/    pi\   
 |  sin |x + --|   
 |      \    3 /   
 |                 
/                  
0
$$\int\limits_{0}^{\frac{\pi}{6}} \frac{1}{\sin^{2}{\left(x + \frac{\pi}{3} \right)}}\, dx$$ 
Integral(1/(sin(x + pi/3)^2), (x, 0, pi/6))
The answer (Indefinite) [src] 
  /                         /x   pi\                
 |                       tan|- + --|                
 |      1                   \2   6 /         1      
 | ------------ dx = C + ----------- - -------------
 |    2/    pi\               2             /x   pi\
 | sin |x + --|                        2*tan|- + --|
 |     \    3 /                             \2   6 /
 |                                                  
/
$$\int \frac{1}{\sin^{2}{\left(x + \frac{\pi}{3} \right)}}\, dx = C + \frac{\tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}{2} - \frac{1}{2 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___
\/ 3 
-----
  3
$$\frac{\sqrt{3}}{3}$$ 
=
= 
  ___
\/ 3 
-----
  3
$$\frac{\sqrt{3}}{3}$$ 
sqrt(3)/3
Numerical answer [src] 
0.577350269189626
0.577350269189626

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

    © Mister Exam – Calculator