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Integral of 3x^2+6x*y^2 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
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 |  \3*x  + 6*x*y / dx
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$$\int\limits_{0}^{1} \left(3 x^{2} + 6 x y^{2}\right)\, dx$$
Integral(3*x^2 + (6*x)*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:

      1. The integral of is when :

      So, the result is:

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

      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:

      So, the result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                     
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 | /   2        2\           3      2  2
 | \3*x  + 6*x*y / dx = C + x  + 3*x *y 
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$$\int \left(3 x^{2} + 6 x y^{2}\right)\, dx = C + x^{3} + 3 x^{2} y^{2}$$
The answer [src]
       2
1 + 3*y 
$$3 y^{2} + 1$$
=
=
       2
1 + 3*y 
$$3 y^{2} + 1$$
1 + 3*y^2

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