What is the integral of x21^x ?

The integral of x21^x is (21^xx)/(ln(21))-(21^x)/(ln^2(21))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x21^x

\int x 2 1^{x} d x

\frac{2 1 ^{x} x}{ln ( 21 )} - \frac{2 1 ^{x}}{ln ^{2} ( 21 )} + C

Solution steps

\int x \cdot 2 1^{x} d x

Apply Integration By Parts

= \frac{2 1 ^{x} x}{ln ( 21 )} - \int \frac{2 1 ^{x}}{ln ( 21 )} d x

\int \frac{2 1 ^{x}}{ln ( 21 )} d x = \frac{2 1 ^{x}}{ln ^{2} ( 21 )}

= \frac{2 1 ^{x} x}{ln ( 21 )} - \frac{2 1 ^{x}}{ln ^{2} ( 21 )}

Add a constant to the solution

= \frac{2 1 ^{x} x}{ln ( 21 )} - \frac{2 1 ^{x}}{ln ^{2} ( 21 )} + C

\int - \frac{58}{( 3 x + 2 ) ^{2}} d x

\int \frac{x - 48}{x ^{2} - x - 6} d x

\int + sin (6 x) cos (6 x) d x

\int 8 y^{7} - \frac{1}{2} y + y^{\frac{1}{3}} d y

\int \frac{1}{x ^{2} 4 + 9 x ^{2}} d x

What is the integral of x21^x ?
The integral of x21^x is (21^xx)/(ln(21))-(21^x)/(ln^2(21))+C