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Solving integrals/ 2xy+(y^2)

Integral of 2xy+(y^2) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
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∫01(2xy+y2) dx\int\limits_{0}^{1} \left(2 x y + y^{2}\right)\, dx 
Integral(2*x*y + y^2, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

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

      ∫2xy dx=2y∫x dx\int 2 x y\, dx = 2 y \int x\, dx

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

      So, the result is: x2yx^{2} y

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

      ∫y2 dx=xy2\int y^{2}\, dx = x y^{2}

    The result is: x2y+xy2x^{2} y + x y^{2}

  2. Now simplify:

    xy(x+y)x y \left(x + y\right)

  3. Add the constant of integration:

    xy(x+y)+constantx y \left(x + y\right)+ \mathrm{constant}

The answer is:

xy(x+y)+constantx y \left(x + y\right)+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | \2*x*y + y / dx = C + x*y  + y*x 
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∫(2xy+y2) dx=C+x2y+xy2\int \left(2 x y + y^{2}\right)\, dx = C + x^{2} y + x y^{2}
Simplify
The answer [src] 
     2
y + y
y2+yy^{2} + y 
=
= 
     2
y + y
y2+yy^{2} + y
Упростить

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

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