integral of sqrt(2^{4x)}

解答

\int 2^{4 x} d x

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

求解步骤

\int 2^{4 x} d x

化简

2^{4 x} : 4^{x}

= \int 4^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{4 ^{x}}{ln ( 4 )}

化简

\frac{4 ^{x}}{ln ( 4 )} : \frac{2 ^{2 x - 1}}{ln ( 2 )}

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

解答补常数

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

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