Mister Exam

Other calculators

Solving integrals/ ((y^5)*dy)/y+2

Integral of ((y^5)*dy)/y+2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |  / 5    \   
 |  |y     |   
 |  |-- + 2| dy
 |  \y     /   
 |             
/              
-1
∫−11(2+y5y) dy\int\limits_{-1}^{1} \left(2 + \frac{y^{5}}{y}\right)\, dy 
Integral(y^5/y + 2, (y, -1, 1))
Detail solution

  1. Integrate term-by-term:

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

      ∫2 dy=2y\int 2\, dy = 2 y

    1. Don't know the steps in finding this integral.

      But the integral is

      y55\frac{y^{5}}{5}

    The result is: y55+2y\frac{y^{5}}{5} + 2 y

  2. Now simplify:

    y(y4+10)5\frac{y \left(y^{4} + 10\right)}{5}

  3. Add the constant of integration:

    y(y4+10)5+constant\frac{y \left(y^{4} + 10\right)}{5}+ \mathrm{constant}

The answer is:

y(y4+10)5+constant\frac{y \left(y^{4} + 10\right)}{5}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                          
 |                           
 | / 5    \                 5
 | |y     |                y 
 | |-- + 2| dy = C + 2*y + --
 | \y     /                5 
 |                           
/
∫(2+y5y) dy=C+y55+2y\int \left(2 + \frac{y^{5}}{y}\right)\, dy = C + \frac{y^{5}}{5} + 2 y
Simplify
The graph
-1.0-0.8-0.6-0.4-0.21.00.00.20.40.60.85-5
Plot the graph f(x)
The answer [src] 
22/5
225\frac{22}{5} 
=
= 
22/5
225\frac{22}{5} 
22/5

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

    © Mister Exam – Calculator