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

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

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integral of (2^x)/(ln(2))x

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

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

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

Add a constant to the solution

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

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\int_{0}^{2} 2 d x

f (x) = (x + 2) (e^{- x})

\int 3 x cos (9 x) d x

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