Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 1/(1+x^5)
Integral of 3*exp(-3*x)
Integral of 2*x/(1+x)
Integral of (x*x)*exp(-x/2)
Identical expressions
(cosxdx)/sqrt2sinx+ one
( co sinus of e of xdx) divide by square root of 2 sinus of x plus 1
( co sinus of e of xdx) divide by square root of 2 sinus of x plus one
(cosxdx)/√2sinx+1
cosxdx/sqrt2sinx+1
(cosxdx) divide by sqrt2sinx+1
Similar expressions
(cosxdx)/sqrt2sinx-1

Integral of (cosxdx)/sqrt2sinx+1 dx

The solution

You have entered [src]

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

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

Integral(cos(x)/sqrt(2*sin(x)) + 1, (x, 0, pi))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
1. Let $u = \sqrt{2 \sin{\left(x \right)}}$ .
  
  Then let $du = \frac{\sqrt{2} \cos{\left(x \right)} dx}{2 \sqrt{\sin{\left(x \right)}}}$ and substitute $du$ :
  
  $\int 1\, du$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, du = u$
  Now substitute $u$ back in:
  
  $\sqrt{2 \sin{\left(x \right)}}$
The result is: $x + \sqrt{2 \sin{\left(x \right)}}$
Now simplify:

$x + \sqrt{2} \sqrt{\sin{\left(x \right)}}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

pi

$$\pi$$

pi

$$\pi$$

pi

Numerical answer [src]

3.14159266858903

3.14159266858903

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (cosxdx)/sqrt2sinx+1 dx

Limits of integration:

The graph:

Piecewise:

The solution