What is the integral of x*2^x ?

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

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integral of x*2^x

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

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

Solution steps

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

Apply Integration By Parts

: \frac{2 ^{x} x}{ln ( 2 )} - \int \frac{2 ^{x}}{ln ( 2 )} d x

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

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

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

Add a constant to the solution

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

\int 4 cos (4 x) d x

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\frac{d}{d x} (x^{5} + 4 x^{2} - 1)

k = 2 \sum \infty \frac{1}{k ( ln ( k ) )}

- 6 x

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