What is the integral from-infinity to 6 of xe^{x/2} ?

The integral from-infinity to 6 of xe^{x/2} is 8e^3

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integral from-infinity to 6 of xe^{x/2}

\int_{- \infty}^{6} x e^{\frac{x}{2}} d x

8 e^{3}

Decimal Notation

160.68429 \dots

Solution steps

\int_{- \infty}^{6} x e^{\frac{x}{2}} d x

Compute the indefinite integral:

\int x e^{\frac{x}{2}} d x = 4 (\frac{1}{2} e^{\frac{x}{2}} x - e^{\frac{x}{2}}) + C

Compute the boundaries:

\int_{- \infty}^{6} x e^{\frac{x}{2}} d x = 8 e^{3} - 0

= 8 e^{3} - 0

Simplify

= 8 e^{3}

y^{^{'}} = \frac{1}{1 + y}

x^{2} (1 - 3 x)

x \to 1 lim (- (3))

\frac{d}{d x} (ln (x) x)

\int_{0}^{\infty} \frac{1}{2 ^{x}} d x

What is the integral from-infinity to 6 of xe^{x/2} ?
The integral from-infinity to 6 of xe^{x/2} is 8e^3