What is the integral of x/(2^x) ?

The integral of x/(2^x) is -x/(ln(2)*2^x)-1/(ln^2(2)*2^x)+C

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integral of x/(2^x)

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

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

Solution steps

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

Apply Integration By Parts

: - \frac{x}{ln ( 2 ) \cdot 2 ^{x}} - \int - \frac{1}{ln ( 2 ) \cdot 2 ^{x}} d x

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{1}{4} cos^{4} (x^{3}) - sin^{2} (6 x))

\int x sinh (2 x) d x

15 e^{x}

\int_{1}^{\infty} \frac{1}{x ^{7}} d x

What is the integral of x/(2^x) ?
The integral of x/(2^x) is -x/(ln(2)*2^x)-1/(ln^2(2)*2^x)+C