What is the integral from y^2 to 2y+3 of (x+y) ?

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

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integral from y^2 to 2y+3 of (x+y)

\int_{y^{2}}^{2 y + 3} (x + y) d x

y (3 + 2 y) - y^{3} + \frac{( 3 + 2 y ) ^{2} - y ^{4}}{2}

Solution steps

\int_{y^{2}}^{2 y + 3} 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_{y^{2}}^{3 + 2 y} y d x + \int_{y^{2}}^{3 + 2 y} x d x

\int_{y^{2}}^{3 + 2 y} y d x = y (3 + 2 y) - y^{3}

\int_{y^{2}}^{3 + 2 y} x d x = \frac{( 3 + 2 y ) ^{2} - y ^{4}}{2}

= y (3 + 2 y) - y^{3} + \frac{( 3 + 2 y ) ^{2} - y ^{4}}{2}

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