What is the integral from-infinity to 0 of xe^{4x} ?

The integral from-infinity to 0 of xe^{4x} is -1/16

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integral from-infinity to 0 of xe^{4x}

\int_{- \infty}^{0} x e^{4 x} d x

- \frac{1}{16}

Decimal Notation

- 0.0625

Solution steps

\int_{- \infty}^{0} x e^{4 x} d x

Compute the indefinite integral:

\int x e^{4 x} d x = \frac{1}{16} (e^{4 x} \cdot 4 x - e^{4 x}) + C

Compute the boundaries:

\int_{- \infty}^{0} x e^{4 x} d x = - \frac{1}{16} - 0

= - \frac{1}{16} - 0

Simplify

= - \frac{1}{16}

\int x^{4} (1 - x^{5})^{7} d x

\frac{\partial}{\partial x} (w x + 2 y + 3 z)

x \to 2 lim (\frac{[ x - 2 ]}{x - 2})

\frac{d}{d x} (\frac{a ^{2} - x ^{3}}{b ^{2}})

x = 7 y^{2}, x = 8 + 5 y^{2}

What is the integral from-infinity to 0 of xe^{4x} ?
The integral from-infinity to 0 of xe^{4x} is -1/16