integral of (4^{ln(x)})/x

解答

\int \frac{4 ^{l n (x)}}{x} d x

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

求解步骤

\int \frac{4 ^{l n (x)}}{x} d x

使用换元积分法

= \int 4^{u} d u

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

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

u = ln (x)

代回

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

化简

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

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

解答补常数

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

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