What is the integral of (7x)/(e^x) ?

The integral of (7x)/(e^x) is 7(-x/(e^x)-1/(e^x))+C

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integral of (7x)/(e^x)

\int \frac{7 x}{e ^{x}} d x

7 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}}) + C

Solution steps

\int \frac{7 x}{e ^{x}} d x

Take the constant out:

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

= 7 \cdot \int \frac{x}{e ^{x}} d x

Apply Integration By Parts

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

= 7 (- \frac{x}{e ^{x}} - \int - \frac{1}{e ^{x}} d x)

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

= 7 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}})

Add a constant to the solution

= 7 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}}) + C

y = sin (x y) + π, (1, π)

f (x) = x^{4} + 3 e^{x}, at x = 0

\int 42 x (x + 7)^{5} d x

\frac{d}{d x} (26 (2 e^{x^{2}} x^{2} + e^{x^{2}}))

y^{^{'}} = 3 y^{2} + x y^{2}, y (0) = 1

What is the integral of (7x)/(e^x) ?
The integral of (7x)/(e^x) is 7(-x/(e^x)-1/(e^x))+C