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

The integral of 2^{(ln(x))/(ln(2))} is 2^{(ln(x)}{ln(2)}}x-\frac{x^2)/2+C

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

\int 2^{\frac{l n ( x )}{l n ( 2 )}} d x

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

Solution steps

\int 2^{\frac{l n ( x )}{l n ( 2 )}} d x

Apply Integration By Parts

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

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

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

= 2^{\frac{l n ( x )}{l n ( 2 )}} x - \frac{x ^{2}}{2}

Add a constant to the solution

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

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What is the integral of 2^{(ln(x))/(ln(2))} ?
The integral of 2^{(ln(x))/(ln(2))} is 2^{(ln(x)}{ln(2)}}x-\frac{x^2)/2+C