What is the integral from 1 to 3 of 5xe^x ?

The integral from 1 to 3 of 5xe^x is 10e^3

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integral from 1 to 3 of 5xe^x

\int_{1}^{3} 5 x e^{x} d x

10 e^{3}

Decimal

200.85536 \dots

Solution steps

\int_{1}^{3} 5 x e^{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int_{1}^{3} x e^{x} d x

Apply Integration By Parts

= 5 [e^{x} x - \int e^{x} d x]_{1}^{3}

\int e^{x} d x = e^{x}

= 5 [e^{x} x - e^{x}]_{1}^{3}

Compute the boundaries:

2 e^{3}

= 5 \cdot 2 e^{3}

Simplify

= 10 e^{3}

\int x^{2} - 25 d x

d er i v a t i v e f (x) = (x + \frac{1}{3 x})^{2}

x \to \infty lim (e^{- 6 x} cos (x))

x y^{2} y^{^{'}} = y^{3} - 3 x^{3}, y (1) = 6

a re a x = 8 y^{2}, x = 2 + 6 y^{2}

What is the integral from 1 to 3 of 5xe^x ?
The integral from 1 to 3 of 5xe^x is 10e^3