What is the integral of (5x)/(e^x) ?

The integral of (5x)/(e^x) is 5(-x/(e^x)-1/(e^x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (5x)/(e^x)

\int \frac{5 x}{e ^{x}} d x

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

Solution steps

\int \frac{5 x}{e ^{x}} d x

Take the constant out:

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

= 5 \cdot \int \frac{x}{e ^{x}} d x

Apply Integration By Parts

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

= 5 (- \frac{x}{e ^{x}} - \int - \frac{1}{e ^{x}} d x)

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

= 5 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}})

Add a constant to the solution

= 5 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}}) + C

\int ln (3 x^{3}) d x

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

\int \frac{1}{a u ^{2} + b u + c} d u

\int \frac{1}{x \cdot ( 1 + ln ( x ) )} d x

What is the integral of (5x)/(e^x) ?
The integral of (5x)/(e^x) is 5(-x/(e^x)-1/(e^x))+C