Mister Exam

Integral of x-3y dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
    2               
   x                
    /               
   |                
   |    (x - 3*y) dy
   |                
  /                 
   ___              
-\/ x               
-------             
 1 + x              
$$\int\limits_{- \frac{\sqrt{x}}{x + 1}}^{x^{2}} \left(x - 3 y\right)\, dy$$
Integral(x - 3*y, (y, -sqrt(x)/(1 + x), x^2))
Detail solution
  1. Integrate term-by-term:

    1. The integral of a constant is the constant times the variable of integration:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is when :

      So, the result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                      2      
 |                    3*y       
 | (x - 3*y) dy = C - ---- + x*y
 |                     2        
/                               
$$\int \left(x - 3 y\right)\, dy = C + x y - \frac{3 y^{2}}{2}$$
The answer [src]
        4     3/2             
 3   3*x     x         3*x    
x  - ---- + ----- + ----------
      2     1 + x            2
                    2*(1 + x) 
$$\frac{x^{\frac{3}{2}}}{x + 1} - \frac{3 x^{4}}{2} + x^{3} + \frac{3 x}{2 \left(x + 1\right)^{2}}$$
=
=
        4     3/2             
 3   3*x     x         3*x    
x  - ---- + ----- + ----------
      2     1 + x            2
                    2*(1 + x) 
$$\frac{x^{\frac{3}{2}}}{x + 1} - \frac{3 x^{4}}{2} + x^{3} + \frac{3 x}{2 \left(x + 1\right)^{2}}$$
x^3 - 3*x^4/2 + x^(3/2)/(1 + x) + 3*x/(2*(1 + x)^2)

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