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

The integral from-infinity to 6 of xe^{x/3} is 9e^2

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integral from-infinity to 6 of xe^{x/3}

\int_{- \infty}^{6} x e^{\frac{x}{3}} d x

9 e^{2}

Solution steps

\int_{- \infty}^{6} x e^{\frac{x}{3}} d x

Compute the indefinite integral:

\int x e^{\frac{x}{3}} d x = 3 e^{\frac{x}{3}} x - 9 e^{\frac{x}{3}} + C

Compute the boundaries:

\int_{- \infty}^{6} x e^{\frac{x}{3}} d x = 9 e^{2} - 0

= 9 e^{2} - 0

Simplify

= 9 e^{2}

y^{^{'}} = cos^{2} (t) cos^{2} (2 y)

x \to 0 lim (1 - cot (x))

\frac{t}{( t - 7 ) ^{2}}

\frac{d y}{d x} = sin (x + y)

f (x) = (4 x - 1)^{- 2}

What is the integral from-infinity to 6 of xe^{x/3} ?
The integral from-infinity to 6 of xe^{x/3} is 9e^2