What is the integral of x*3^x ?

The integral of x*3^x is (3^xx)/(ln(3))-(3^x)/(ln^2(3))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x*3^x

integral

x \cdot 3^{x}

\frac{3 ^{x} x}{ln ( 3 )} - \frac{3 ^{x}}{ln ^{2} ( 3 )} + C

Solution steps

\int x \cdot 3^{x} d x

Apply Integration By Parts

= \frac{3 ^{x} x}{ln ( 3 )} - \int \frac{3 ^{x}}{ln ( 3 )} d x

\int \frac{3 ^{x}}{ln ( 3 )} d x = \frac{3 ^{x}}{ln ^{2} ( 3 )}

= \frac{3 ^{x} x}{ln ( 3 )} - \frac{3 ^{x}}{ln ^{2} ( 3 )}

Add a constant to the solution

= \frac{3 ^{x} x}{ln ( 3 )} - \frac{3 ^{x}}{ln ^{2} ( 3 )} + C

What is the integral of x*3^x ?
The integral of x*3^x is (3^xx)/(ln(3))-(3^x)/(ln^2(3))+C