What is the integral from y^2-4 to 5 of (x+2y) ?

The integral from y^2-4 to 5 of (x+2y) is (-y^4+8y^2+9)/2+18y-2y^3

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integral from y^2-4 to 5 of (x+2y)

\int_{y^{2} - 4}^{5} (x + 2 y) d x

\frac{- y ^{4} + 8 y ^{2} + 9}{2} + 18 y - 2 y^{3}

Solution steps

\int_{y^{2} - 4}^{5} x + 2 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_{- 4 + y^{2}}^{5} x d x + \int_{- 4 + y^{2}}^{5} 2 y d x

\int_{- 4 + y^{2}}^{5} x d x = \frac{- y ^{4} + 8 y ^{2} + 9}{2}

\int_{- 4 + y^{2}}^{5} 2 y d x = 18 y - 2 y^{3}

= \frac{- y ^{4} + 8 y ^{2} + 9}{2} + 18 y - 2 y^{3}

\int_{0}^{1} 2 π x 4 x - x^{2} d x

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\int_{4}^{5} \frac{1}{x ^{2} - 5 x + 6} d x

\int_{2}^{14} \frac{1}{x} d x

What is the integral from y^2-4 to 5 of (x+2y) ?
The integral from y^2-4 to 5 of (x+2y) is (-y^4+8y^2+9)/2+18y-2y^3