integral of 4^{7x}

解答

\int 4^{7 x} d x

\frac{2 ^{14 x - 1}}{7 ln ( 2 )} + C

求解步骤

\int 4^{7 x} d x

化简

4^{7 x} : 1638 4^{x}

= \int 1638 4^{x} d x

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

= \frac{1638 4 ^{x}}{ln ( 16384 )}

化简

\frac{1638 4 ^{x}}{ln ( 16384 )} : \frac{2 ^{14 x - 1}}{7 ln ( 2 )}

= \frac{2 ^{14 x - 1}}{7 ln ( 2 )}

解答补常数

= \frac{2 ^{14 x - 1}}{7 ln ( 2 )} + C