Mister Exam

Other calculators

Integral of (x^2+3x*y)*d*y dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                    
  /                    
 |                     
 |  / 2        \       
 |  \x  + 3*x*y/*d*y dx
 |                     
/                      
d                      
$$\int\limits_{d}^{1} d y \left(x^{2} + 3 x y\right)\, dx$$
Integral((x^2 + 3*x*y)*d*y, (x, d, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Integrate term-by-term:

      1. The integral of is when :

      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:

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                           
 |                               / 3        2\
 | / 2        \                  |x    3*y*x |
 | \x  + 3*x*y/*d*y dx = C + d*y*|-- + ------|
 |                               \3      2   /
/                                             
$$d\,y\,\left({{3\,x^2\,y}\over{2}}+{{x^3}\over{3}}\right)$$
The answer [src]
     3  2      4              2
  3*d *y    y*d    d*y   3*d*y 
- ------- - ---- + --- + ------
     2       3      3      2   
$$d\,y\,\left({{9\,y+2}\over{6}}-{{9\,d^2\,y+2\,d^3}\over{6}}\right)$$
=
=
     3  2      4              2
  3*d *y    y*d    d*y   3*d*y 
- ------- - ---- + --- + ------
     2       3      3      2   
$$- \frac{d^{4} y}{3} - \frac{3 d^{3} y^{2}}{2} + \frac{3 d y^{2}}{2} + \frac{d y}{3}$$

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