What is the integral of-x/(e^x) ?

The integral of-x/(e^x) is x/(e^x)+1/(e^x)+C

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integral of-x/(e^x)

\int - \frac{x}{e ^{x}} d x

\frac{x}{e ^{x}} + \frac{1}{e ^{x}} + C

Solution steps

\int - \frac{x}{e ^{x}} d x

Take the constant out:

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

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

Apply Integration By Parts

: - \frac{x}{e ^{x}} - \int - \frac{1}{e ^{x}} d x

= - (- \frac{x}{e ^{x}} - \int - \frac{1}{e ^{x}} d x)

\int - \frac{1}{e ^{x}} d x = \frac{1}{e ^{x}}

= - (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}})

Simplify

= \frac{x}{e ^{x}} + \frac{1}{e ^{x}}

Add a constant to the solution

= \frac{x}{e ^{x}} + \frac{1}{e ^{x}} + C

\int (4 - x)^{2} d x

e^{\frac{- x ^{2}}{2}}

\frac{d}{d x} (\frac{4 x}{( x ^{2} + 1 ) ^{2}})

\int_{0}^{1} - \frac{6 y}{e ^{2 y}} d y

x \to 3 lim (e^{\frac{7}{( x - 3 )}})