What is the integral from y to 2y of 8x+e^y ?

The integral from y to 2y of 8x+e^y is ye^y+12y^2

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integral from y to 2y of 8x+e^y

\int_{y}^{2 y} 8 x + e^{y} d x

y e^{y} + 12 y^{2}

Solution steps

\int_{y}^{2 y} 8 x + e^{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 y} e^{y} d x + \int_{y}^{2 y} 8 x d x

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

\int_{y}^{2 y} 8 x d x = 12 y^{2}

= y e^{y} + 12 y^{2}

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\int_{2}^{4} - x^{3} + 6 x^{2} - 8 x d x

\int_{0}^{1} tan (π) x d x

\int_{3}^{6} 1 0^{8} (\frac{t ^{2}}{3} + 1) d t

\int_{0}^{10} - 6 x^{2} - 12 x + 720 d x

What is the integral from y to 2y of 8x+e^y ?
The integral from y to 2y of 8x+e^y is ye^y+12y^2