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

900 x - 0.1 x^{2}

\int \frac{cos ( 3 x )}{sin ^{4} ( 3 x )} d x

f (x) = 2 x^{2} - 18 x + 5, at x = 0

x \to \infty lim (\frac{3 x ^{2} - x - 2}{5 x ^{2} - 4 x + 1})

f (x) = \frac{x ^{2}}{3 + 8 x}

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