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

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

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

e^{3 x} x + C

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

= e^{3 x} x

Add a constant to the solution

= e^{3 x} x + C

\frac{d}{d x} (arccos (x y))

\frac{d}{d x} (5 (3 x^{2} + 5 x) (1 - x)^{2})

\frac{d}{d x} (\frac{3}{x ^{3}} - \frac{4}{x ^{2}})

\frac{d}{d x} (x^{5} e^{7 x})

x \to 1 lim ((x - 1)^{3 x - 3})

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