What is the integral from 0 to 1 of (x^2+5)(e^{-x}) ?

The integral from 0 to 1 of (x^2+5)(e^{-x}) is -(10)/e+7

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integral from 0 to 1 of (x^2+5)(e^{-x})

\int_{0}^{1} (x^{2} + 5) (e^{- x}) d x

- \frac{10}{e} + 7

Decimal Notation

3.32120 \dots

Solution steps

\int_{0}^{1} (x^{2} + 5) e^{- x} d x

Apply Integration By Parts

: [- e^{- x} (x^{2} + 5) - \int - 2 e^{- x} x d x]_{0}^{1}

= [- e^{- x} (x^{2} + 5) - \int - 2 e^{- x} x d x]_{0}^{1}

\int - 2 e^{- x} x d x = - 2 (- e^{- x} x - e^{- x})

= [- e^{- x} (x^{2} + 5) - (- 2 (- e^{- x} x - e^{- x}))]_{0}^{1}

Simplify

[- e^{- x} (x^{2} + 5) - (- 2 (- e^{- x} x - e^{- x}))]_{0}^{1} : [- e^{- x} x^{2} - 2 e^{- x} x - 7 e^{- x}]_{0}^{1}

= [- e^{- x} x^{2} - 2 e^{- x} x - 7 e^{- x}]_{0}^{1}

Compute the boundaries:

- \frac{10}{e} + 7

= - \frac{10}{e} + 7

\frac{d}{d θ} (θ^{2})

y^{^{'}} = \frac{y}{3 x} - \frac{x}{3 y}

\int - cos (x) sin (n x) d x

\frac{\partial}{\partial x} (3 x cos (x y))

g (x) = x (x^{3} - x)

What is the integral from 0 to 1 of (x^2+5)(e^{-x}) ?
The integral from 0 to 1 of (x^2+5)(e^{-x}) is -(10)/e+7