Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of (x+2)e^x
Integral of √(1+x²)
Integral of 1/tanx
Integral of a
Identical expressions
sin(y)+y*sin(x)+ one /x
sinus of (y) plus y multiply by sinus of (x) plus 1 divide by x
sinus of (y) plus y multiply by sinus of (x) plus one divide by x
sin(y)+ysin(x)+1/x
siny+ysinx+1/x
sin(y)+y*sin(x)+1 divide by x
sin(y)+y*sin(x)+1/xdx
Similar expressions
sin(y)-y*sin(x)+1/x
sin(y)+y*sin(x)-1/x
sin(y)+y*sin(x)+(1/x)
sin(y)+y*sinx+1/x

Integral of sin(y)+y*sin(x)+1/x dx

The solution

You have entered [src]

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

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

Integral(sin(y) + y*sin(x) + 1/x, (x, 0, x))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int y \sin{\left(x \right)}\, dx = y \int \sin{\left(x \right)}\, dx$
    1. The integral of sine is negative cosine:
      
      $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
    So, the result is: $- y \cos{\left(x \right)}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(y \right)}\, dx = - \cos{\left(y \right)}$
  The result is: $- y \cos{\left(x \right)} - \cos{\left(y \right)}$
1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
The result is: $- y \cos{\left(x \right)} + \log{\left(x \right)} - \cos{\left(y \right)}$
Add the constant of integration:

$- y \cos{\left(x \right)} + \log{\left(x \right)} - \cos{\left(y \right)}+ \mathrm{constant}$

The answer is:

$- y \cos{\left(x \right)} + \log{\left(x \right)} - \cos{\left(y \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

oo + x*sin(y) - y*cos(x) + log(x)

$$x \sin{\left(y \right)} - y \cos{\left(x \right)} + \log{\left(x \right)} + \infty$$

oo + x*sin(y) - y*cos(x) + log(x)

$$x \sin{\left(y \right)} - y \cos{\left(x \right)} + \log{\left(x \right)} + \infty$$

oo + x*sin(y) - y*cos(x) + log(x)

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of sin(y)+y*sin(x)+1/x dx

Limits of integration:

The graph:

Piecewise:

The solution