What is the integral of (x+5)e^{x/2} ?

The integral of (x+5)e^{x/2} is 2e^{x/2}x+6e^{x/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x+5)e^{x/2}

\int (x + 5) e^{\frac{x}{2}} d x

2 e^{\frac{x}{2}} x + 6 e^{\frac{x}{2}} + C

Solution steps

\int (x + 5) e^{\frac{x}{2}} d x

Expand

(x + 5) e^{\frac{x}{2}} : e^{\frac{x}{2}} x + 5 e^{\frac{x}{2}}

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int e^{\frac{x}{2}} x d x = 4 (\frac{1}{2} e^{\frac{x}{2}} x - e^{\frac{x}{2}})

\int 5 e^{\frac{x}{2}} d x = 10 e^{\frac{x}{2}}

= 4 (\frac{1}{2} e^{\frac{x}{2}} x - e^{\frac{x}{2}}) + 10 e^{\frac{x}{2}}

Simplify

4 (\frac{1}{2} e^{\frac{x}{2}} x - e^{\frac{x}{2}}) + 10 e^{\frac{x}{2}} : 2 e^{\frac{x}{2}} x + 6 e^{\frac{x}{2}}

= 2 e^{\frac{x}{2}} x + 6 e^{\frac{x}{2}}

Add a constant to the solution

= 2 e^{\frac{x}{2}} x + 6 e^{\frac{x}{2}} + C

\int (2 x + 1) (x^{2} + x + 1)^{3} d x

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

\int 36 e^{6 x} 5 + e^{6 x} d x

\int \frac{ln ( x ^{24} )}{x} d x

\int \frac{5}{3 x ^{4}} d x

What is the integral of (x+5)e^{x/2} ?
The integral of (x+5)e^{x/2} is 2e^{x/2}x+6e^{x/2}+C