integral of 5^{2x-1}-2^{3x}

解答

\int 5^{2 x - 1} - 2^{3 x} d x

\frac{5 ^{2 x - 1}}{2 ln ( 5 )} - \frac{8 ^{x}}{3 ln ( 2 )} + C

求解步骤

\int 5^{2 x - 1} - 2^{3 x} d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 5^{2 x - 1} d x - \int 2^{3 x} d x

\int 5^{2 x - 1} d x = \frac{5 ^{2 x - 1}}{2 ln ( 5 )}

\int 2^{3 x} d x = \frac{8 ^{x}}{3 ln ( 2 )}

= \frac{5 ^{2 x - 1}}{2 ln ( 5 )} - \frac{8 ^{x}}{3 ln ( 2 )}

解答补常数

= \frac{5 ^{2 x - 1}}{2 ln ( 5 )} - \frac{8 ^{x}}{3 ln ( 2 )} + C

\int (5 - 2 x)^{7} d x

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