What is the integral of 6/7 (x^2+(xy)/2) ?

The integral of 6/7 (x^2+(xy)/2) is 6/7 ((xy^2)/4+x^2y)+C

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integral of 6/7 (x^2+(xy)/2)

\int \frac{6}{7} (x^{2} + \frac{x y}{2}) d y

\frac{6}{7} (\frac{x y ^{2}}{4} + x^{2} y) + C

Solution steps

\int \frac{6}{7} (x^{2} + \frac{x y}{2}) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{6}{7} \cdot \int \frac{x y}{2} + x^{2} d y

Apply the Sum Rule:

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

= \frac{6}{7} (\int \frac{x y}{2} d y + \int x^{2} d y)

\int \frac{x y}{2} d y = \frac{x y ^{2}}{4}

\int x^{2} d y = x^{2} y

= \frac{6}{7} (\frac{x y ^{2}}{4} + x^{2} y)

Add a constant to the solution

= \frac{6}{7} (\frac{x y ^{2}}{4} + x^{2} y) + C

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What is the integral of 6/7 (x^2+(xy)/2) ?
The integral of 6/7 (x^2+(xy)/2) is 6/7 ((xy^2)/4+x^2y)+C