What is the integral from 2 to 3 of x^3+e^{-2x}-5 ?

The integral from 2 to 3 of x^3+e^{-2x}-5 is 45/4+(e^2-1)/(2e^6)

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integral from 2 to 3 of x^3+e^{-2x}-5

\int_{2}^{3} x^{3} + e^{- 2 x} - 5 d x

\frac{45}{4} + \frac{e ^{2} - 1}{2 e ^{6}}

Decimal

11.25791 \dots

Solution steps

\int_{2}^{3} x^{3} + e^{- 2 x} - 5 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_{2}^{3} x^{3} d x + \int_{2}^{3} e^{- 2 x} d x - \int_{2}^{3} 5 d x

\int_{2}^{3} x^{3} d x = \frac{65}{4}

\int_{2}^{3} e^{- 2 x} d x = \frac{e ^{2} - 1}{2 e ^{6}}

\int_{2}^{3} 5 d x = 5

= \frac{65}{4} + \frac{e ^{2} - 1}{2 e ^{6}} - 5

Combine the fractions

- 5 + \frac{65}{4} : \frac{45}{4}

= \frac{45}{4} + \frac{e ^{2} - 1}{2 e ^{6}}

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What is the integral from 2 to 3 of x^3+e^{-2x}-5 ?
The integral from 2 to 3 of x^3+e^{-2x}-5 is 45/4+(e^2-1)/(2e^6)