integral of (8x^4+10cos(x)-2^x)

解答

\int (8 x^{4} + 10 cos (x) - 2^{x}) d x

\frac{8 x ^{5}}{5} + 10 sin (x) - \frac{2 ^{x}}{ln ( 2 )} + C

求解步骤

\int 8 x^{4} + 10 cos (x) - 2^{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 8 x^{4} d x + \int 10 cos (x) d x - \int 2^{x} d x

\int 8 x^{4} d x = \frac{8 x ^{5}}{5}

\int 10 cos (x) d x = 10 sin (x)

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

= \frac{8 x ^{5}}{5} + 10 sin (x) - \frac{2 ^{x}}{ln ( 2 )}

解答补常数

= \frac{8 x ^{5}}{5} + 10 sin (x) - \frac{2 ^{x}}{ln ( 2 )} + C

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