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Solving integrals/ x^2+2*y

Integral of x^2+2*y dx

Limits of integration:

from to
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Piecewise:

The solution

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∫01(x2+2y) dx\int\limits_{0}^{1} \left(x^{2} + 2 y\right)\, dx 
Integral(x^2 + 2*y, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

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

      ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

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

      ∫2y dx=2xy\int 2 y\, dx = 2 x y

    The result is: x33+2xy\frac{x^{3}}{3} + 2 x y

  2. Now simplify:

    x(x2+6y)3\frac{x \left(x^{2} + 6 y\right)}{3}

  3. Add the constant of integration:

    x(x2+6y)3+constant\frac{x \left(x^{2} + 6 y\right)}{3}+ \mathrm{constant}

The answer is:

x(x2+6y)3+constant\frac{x \left(x^{2} + 6 y\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(x2+2y) dx=C+x33+2xy\int \left(x^{2} + 2 y\right)\, dx = C + \frac{x^{3}}{3} + 2 x y
Simplify
The answer [src] 
1/3 + 2*y
2y+132 y + \frac{1}{3} 
=
= 
1/3 + 2*y
2y+132 y + \frac{1}{3} 
1/3 + 2*y

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

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