integral from 0 to 1 of 6^{3x}

解答

\int_{0}^{1} 6^{3 x} d x

\frac{215}{3 ln ( 6 )}

十进制

39.99792 \dots

求解步骤

\int_{0}^{1} 6^{3 x} d x

化简

6^{3 x} : 21 6^{x}

= \int_{0}^{1} 21 6^{x} d x

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

= [\frac{21 6 ^{x}}{ln ( 216 )}]_{0}^{1}

\frac{21 6 ^{x}}{ln ( 216 )} = \frac{8 ^{x} \cdot 3 ^{3 x - 1}}{ln ( 6 )}

= [\frac{8 ^{x} \cdot 3 ^{3 x - 1}}{ln ( 6 )}]_{0}^{1}

带入上下限计算后得:

\frac{215}{3 ln ( 6 )}

= \frac{215}{3 ln ( 6 )}

\int \frac{x ^{2} - 49}{x ^{3}} d x

\frac{\partial}{\partial x} (4 x y e^{x})

x \to 2 lim (3 x^{4} + 2 x^{2} - x + 1)

x \to - 8 lim (x^{3})

y^{^{''}} + 25 y = e^{- t}