What is the integral from 2 to 4 of x^2y+y^2x+x+y ?

The integral from 2 to 4 of x^2y+y^2x+x+y is 2y+6+y^2*6+(56y)/3

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integral from 2 to 4 of x^2y+y^2x+x+y

\int_{2}^{4} x^{2} y + y^{2} x + x + y d x

2 y + 6 + y^{2} \cdot 6 + \frac{56 y}{3}

Solution steps

\int_{2}^{4} x^{2} y + y^{2} x + x + y d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{2}^{4} y d x + \int_{2}^{4} x d x + \int_{2}^{4} y^{2} x d x + \int_{2}^{4} y x^{2} d x

\int_{2}^{4} y d x = 2 y

\int_{2}^{4} x d x = 6

\int_{2}^{4} y^{2} x d x = y^{2} \cdot 6

\int_{2}^{4} y x^{2} d x = \frac{56 y}{3}

= 2 y + 6 + y^{2} \cdot 6 + \frac{56 y}{3}

\frac{1}{1 + x ^{- 1}}

y^{^{''}} - 5 y^{^{'}} = 0, y (0) = 6, y^{^{'}} (0) = - 9

\frac{\partial}{\partial x} (ln (x^{4} - y^{4}))

\frac{d}{d x} (I n^{4} x)

\frac{5 x + 1}{5 x - 1}

What is the integral from 2 to 4 of x^2y+y^2x+x+y ?
The integral from 2 to 4 of x^2y+y^2x+x+y is 2y+6+y^2*6+(56y)/3