What is the integral from 2 to 4 of xe^{x/2} ?

The integral from 2 to 4 of xe^{x/2} is 4e^2

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integral from 2 to 4 of xe^{x/2}

\int_{2}^{4} x e^{\frac{x}{2}} d x

4 e^{2}

Decimal

29.55622 \dots

Solution steps

\int_{2}^{4} x e^{\frac{x}{2}} d x

Apply u-substitution

: \int_{1}^{2} 4 e^{u} u d u

= \int_{1}^{2} 4 e^{u} u d u

Take the constant out:

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

= 4 \cdot \int_{1}^{2} e^{u} u d u

Apply Integration By Parts

: [e^{u} u - \int e^{u} d u]_{1}^{2}

= 4 [e^{u} u - \int e^{u} d u]_{1}^{2}

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

= 4 [e^{u} u - e^{u}]_{1}^{2}

Compute the boundaries:

e^{2}

= 4 e^{2}

f (x) = \frac{1}{2 x - 1}

\int \frac{28}{28 + e ^{x}} d x

2 x \frac{d y}{d x} + y = 6 x

x \to 3 + lim (6 + x)

y = \frac{6}{x ^{2}}, (1, 6)

What is the integral from 2 to 4 of xe^{x/2} ?
The integral from 2 to 4 of xe^{x/2} is 4e^2