Mister Exam

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Integral of d{x}:
Integral of logx/x^2
Integral of cosxsin^2x
Integral of cosx/1+2sinx
Integral of 1/(5-4cos(2x))
Derivative of:
cosx/1+2sinx
Equation:
cosx/1+2sinx
Identical expressions
cosx/ one +2sinx
co sinus of e of x divide by 1 plus 2 sinus of x
co sinus of e of x divide by one plus 2 sinus of x
cosx divide by 1+2sinx
cosx/1+2sinxdx
Similar expressions
cosx/1-2sinx
cosx/(1+2sinx)

Solving integrals/ cosx/1+2sinx

Integral of cosx/1+2sinx dx

The solution

You have entered [src]

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

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

Simplify

Detail solution

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

$\sin{\left(x \right)} - 2 \cos{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\sin{\left(x \right)} - 2 \cos{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                              
 |                                               
 | /cos(x)           \                           
 | |------ + 2*sin(x)| dx = C - 2*cos(x) + sin(x)
 | \  1              /                           
 |                                               
/

$$\sin x-2\,\cos x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

2 - 2*cos(1) + sin(1)

$$\sin 1-2\,\cos 1+2$$

2 - 2*cos(1) + sin(1)

$$- 2 \cos{\left(1 \right)} + \sin{\left(1 \right)} + 2$$

Simplify

Numerical answer [src]

1.76086637307162

1.76086637307162

The graph

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

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Identical expressions

Similar expressions

Integral of cosx/1+2sinx dx

Limits of integration:

The graph:

Piecewise:

The solution