Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of sin²xcos²x
Integral of tg2x
Integral of 1/(x^2-9)
Integral of x*e^(x*y)
Identical expressions
(-3sinx+ two /sin^2x)
( minus 3 sinus of x plus 2 divide by sinus of squared x)
( minus 3 sinus of x plus two divide by sinus of squared x)
(-3sinx+2/sin2x)
-3sinx+2/sin2x
(-3sinx+2/sin²x)
(-3sinx+2/sin to the power of 2x)
-3sinx+2/sin^2x
(-3sinx+2 divide by sin^2x)
(-3sinx+2/sin^2x)dx
Similar expressions
(-3sinx-2/sin^2x)
(3sinx+2/sin^2x)

Integral of (-3sinx+2/sin^2x) dx

The solution

You have entered [src]

  1                         
  /                         
 |                          
 |  /               2   \   
 |  |-3*sin(x) + -------| dx
 |  |               2   |   
 |  \            sin (x)/   
 |                          
/                           
0

$$\int\limits_{0}^{1} \left(- 3 \sin{\left(x \right)} + \frac{2}{\sin^{2}{\left(x \right)}}\right)\, dx$$

Integral(-3*sin(x) + 2/sin(x)^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 3 \sin{\left(x \right)}\right)\, dx = - 3 \int \sin{\left(x \right)}\, dx$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
  So, the result is: $3 \cos{\left(x \right)}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{2}{\sin^{2}{\left(x \right)}}\, dx = 2 \int \frac{1}{\sin^{2}{\left(x \right)}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
  So, the result is: $- \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}$
The result is: $3 \cos{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}$
Now simplify:

$\frac{3 \sin{\left(x \right)} - 2}{\tan{\left(x \right)}}$
Add the constant of integration:

$\frac{3 \sin{\left(x \right)} - 2}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer is:

$\frac{3 \sin{\left(x \right)} - 2}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                  
 |                                                   
 | /               2   \                     2*cos(x)
 | |-3*sin(x) + -------| dx = C + 3*cos(x) - --------
 | |               2   |                      sin(x) 
 | \            sin (x)/                             
 |                                                   
/

$$\int \left(- 3 \sin{\left(x \right)} + \frac{2}{\sin^{2}{\left(x \right)}}\right)\, dx = C + 3 \cos{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

2.75864735589719e+19

2.75864735589719e+19

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (-3sinx+2/sin^2x) dx

Limits of integration:

The graph:

Piecewise:

The solution