Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x²+4
Integral of x^3e^x
Integral of 2x^3+1
Integral of 2*x^2+2/x^4
Identical expressions
sinx/sqrt1+2cosx
sinus of x divide by square root of 1 plus 2 co sinus of e of x
sinx/√1+2cosx
sinx divide by sqrt1+2cosx
sinx/sqrt1+2cosxdx
Similar expressions
sin(x)/(sqrt(1+2cos(x)))
sinx/sqrt1-2cosx

Integral of sinx/sqrt1+2cosx dx

The solution

You have entered [src]

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

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

$$\int \left(\frac{\sin{\left(x \right)}}{\sqrt{1}} + 2 \cos{\left(x \right)}\right)\, dx = C + 2 \sin{\left(x \right)} - \cos{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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

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

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

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

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

Numerical answer [src]

2.14263966374765

2.14263966374765

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of sinx/sqrt1+2cosx dx

Limits of integration:

The graph:

Piecewise:

The solution