What is the integral of e^{3x}(3x+1) ?

The integral of e^{3x}(3x+1) is e^{3x}x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{3x}(3x+1)

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

e^{3 x} x + C

Solution steps

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

Apply Integration By Parts

: e^{3 x} x + \frac{1}{3} e^{3 x} - \int e^{3 x} d x

= e^{3 x} x + \frac{1}{3} e^{3 x} - \int e^{3 x} d x

\int e^{3 x} d x = \frac{1}{3} e^{3 x}

= e^{3 x} x + \frac{1}{3} e^{3 x} - \frac{1}{3} e^{3 x}

Add similar elements:

\frac{1}{3} e^{3 x} - \frac{1}{3} e^{3 x} = 0

= e^{3 x} x

Add a constant to the solution

= e^{3 x} x + C

\int_{0}^{t} cos^{2} (wt) d t

\int 3 a y^{2} d y

\frac{d}{d x} (\frac{x + 5}{x - 1})

x \to 0 lim (sin (\frac{π x}{2}))

\int \frac{3 x ^{2}}{x ^{2} - 5} d x

What is the integral of e^{3x}(3x+1) ?
The integral of e^{3x}(3x+1) is e^{3x}x+C