What is the integral of 2^xx ?

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

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integral of 2^xx

\int 2^{x} x d x

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

Solution steps

\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{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

y^{^{''}} - 2 y^{^{'}} + 5 y = 0, y (π) = 0, y^{^{'}} (π) = 2

f (x) = 3 x^{2}, at x = 4

\frac{d}{d x} (\frac{x + 5}{x})

x^{2} y^{^{''}} + x y^{^{'}} - y = x^{\frac{1}{2}}

x \to \infty lim (\frac{4 ^{x} + 3}{4 ^{x + 1}})

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