Mister Exam

Other calculators

Solving integrals/ 5/sin(x+pi/3)^2

Integral of 5/sin(x+pi/3)^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                
 --                
 3                 
  /                
 |                 
 |       5         
 |  ------------ dx
 |     2/    pi\   
 |  sin |x + --|   
 |      \    3 /   
 |                 
/                  
0
∫0π35sin⁡2(x+π3) dx\int\limits_{0}^{\frac{\pi}{3}} \frac{5}{\sin^{2}{\left(x + \frac{\pi}{3} \right)}}\, dx 
Integral(5/sin(x + pi/3)^2, (x, 0, pi/3))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

    ∫5sin⁡2(x+π3) dx=5∫1sin⁡2(x+π3) dx\int \frac{5}{\sin^{2}{\left(x + \frac{\pi}{3} \right)}}\, dx = 5 \int \frac{1}{\sin^{2}{\left(x + \frac{\pi}{3} \right)}}\, dx

    1. Don't know the steps in finding this integral.

      But the integral is

      tan⁡(x2+π6)2−12tan⁡(x2+π6)\frac{\tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}{2} - \frac{1}{2 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}

    So, the result is: 5tan⁡(x2+π6)2−52tan⁡(x2+π6)\frac{5 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}{2} - \frac{5}{2 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}

  2. Add the constant of integration:

    5tan⁡(x2+π6)2−52tan⁡(x2+π6)+constant\frac{5 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}{2} - \frac{5}{2 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}+ \mathrm{constant}

The answer is:

5tan⁡(x2+π6)2−52tan⁡(x2+π6)+constant\frac{5 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}{2} - \frac{5}{2 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                           /x   pi\
 |                                       5*tan|- + --|
 |      5                      5              \2   6 /
 | ------------ dx = C - ------------- + -------------
 |    2/    pi\               /x   pi\         2      
 | sin |x + --|          2*tan|- + --|                
 |     \    3 /               \2   6 /                
 |                                                    
/
∫5sin⁡2(x+π3) dx=C+5tan⁡(x2+π6)2−52tan⁡(x2+π6)\int \frac{5}{\sin^{2}{\left(x + \frac{\pi}{3} \right)}}\, dx = C + \frac{5 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}{2} - \frac{5}{2 \tan{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}
Simplify
The graph
0.000.100.200.300.400.500.600.700.800.901.00-1010
Plot the graph f(x)
The answer [src] 
     ___
10*\/ 3 
--------
   3
1033\frac{10 \sqrt{3}}{3} 
=
= 
     ___
10*\/ 3 
--------
   3
1033\frac{10 \sqrt{3}}{3} 
10*sqrt(3)/3
Numerical answer [src] 
5.77350269189626
5.77350269189626

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

    © Mister Exam – Calculator