What is the integral from-1 to 3 of (6xy-5e^y) ?

The integral from-1 to 3 of (6xy-5e^y) is -20e^y+24y

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integral from-1 to 3 of (6xy-5e^y)

\int_{- 1}^{3} (6 x y - 5 e^{y}) d x

- 20 e^{y} + 24 y

Solution steps

\int_{- 1}^{3} 6 x y - 5 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_{- 1}^{3} 5 e^{y} d x + \int_{- 1}^{3} 6 y x d x

\int_{- 1}^{3} 5 e^{y} d x = 20 e^{y}

\int_{- 1}^{3} 6 y x d x = 24 y

= - 20 e^{y} + 24 y

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What is the integral from-1 to 3 of (6xy-5e^y) ?
The integral from-1 to 3 of (6xy-5e^y) is -20e^y+24y