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

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

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

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

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

Solution steps

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

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

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

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

\int_{0}^{3} (1 + 2 x)^{2} d x

\int_{0}^{1} x^{2} + x^{4} d x

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

\int_{0}^{1} \frac{x}{x ( 1 - x )} d x

\int_{1}^{3} (x^{2} + x + 4) d x

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