What is the integral of 7/8 xe^{x/(10)} ?

The integral of 7/8 xe^{x/(10)} is 35/4 e^{x/(10)}(x-10)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 7/8 xe^{x/(10)}

\int \frac{7}{8} x e^{\frac{x}{10}} d x

\frac{35}{4} e^{\frac{x}{10}} (x - 10) + C

Solution steps

\int \frac{7}{8} x e^{\frac{x}{10}} d x

Take the constant out:

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

= \frac{7}{8} \cdot \int x e^{\frac{x}{10}} d x

Apply Integration By Parts

: 10 e^{\frac{x}{10}} x - \int 10 e^{\frac{x}{10}} d x

= \frac{7}{8} (10 e^{\frac{x}{10}} x - \int 10 e^{\frac{x}{10}} d x)

\int 10 e^{\frac{x}{10}} d x = 100 e^{\frac{x}{10}}

= \frac{7}{8} (10 e^{\frac{x}{10}} x - 100 e^{\frac{x}{10}})

Simplify

\frac{7}{8} (10 e^{\frac{x}{10}} x - 100 e^{\frac{x}{10}}) : \frac{35}{4} e^{\frac{x}{10}} (x - 10)

= \frac{35}{4} e^{\frac{x}{10}} (x - 10)

Add a constant to the solution

= \frac{35}{4} e^{\frac{x}{10}} (x - 10) + C

\int \frac{x ^{4} + 3 x ^{2} + 4}{x ^{2} + 2 x + 1} d x

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

\int \frac{x}{2 x ^{2} + 5} d x

\int \frac{1}{( x + 2 ) ^{2} + 9} d x

\int - \frac{1200}{x ^{2}} d x

What is the integral of 7/8 xe^{x/(10)} ?
The integral of 7/8 xe^{x/(10)} is 35/4 e^{x/(10)}(x-10)+C