What is the integral of s2^s ?

The integral of s2^s is (2^ss)/(ln(2))-(2^s)/(ln^2(2))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of s2^s

\int s 2^{s} d s

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

Solution steps

\int s \cdot 2^{s} d s

Apply Integration By Parts

= \frac{2 ^{s} s}{ln ( 2 )} - \int \frac{2 ^{s}}{ln ( 2 )} d s

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

= \frac{2 ^{s} s}{ln ( 2 )} - \frac{2 ^{s}}{ln ^{2} ( 2 )}

Add a constant to the solution

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

What is the integral of s2^s ?
The integral of s2^s is (2^ss)/(ln(2))-(2^s)/(ln^2(2))+C