integral of (3^x)/(4^x)

解答

\int \frac{3 ^{x}}{4 ^{x}} d x

\frac{3 ^{x}}{ln ( \frac{3}{4} ) \cdot 4 ^{x}} + C

求解步骤

\int \frac{3 ^{x}}{4 ^{x}} d x

使用指数法则:

\frac{a ^{c}}{b ^{c}} = (\frac{a}{b})^{c}

= \int (\frac{3}{4})^{x} d x

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

= \frac{( \frac{3}{4} ) ^{x}}{ln ( \frac{3}{4} )}

化简

\frac{( \frac{3}{4} ) ^{x}}{ln ( \frac{3}{4} )} : \frac{3 ^{x}}{ln ( \frac{3}{4} ) \cdot 4 ^{x}}

= \frac{3 ^{x}}{ln ( \frac{3}{4} ) \cdot 4 ^{x}}

解答补常数

= \frac{3 ^{x}}{ln ( \frac{3}{4} ) \cdot 4 ^{x}} + C

l a pl a ce t r an s f or m \frac{1}{2} e^{- 4 t} - \frac{1}{2} e^{- 6 t}

x \to 0 - lim (sin (x))

y^{^{''}} + 3 y = x

\int t ln (t + 3) d t

\int \frac{1}{b} sin (b x) d x