integral of 2^x+2x

解答

\int 2^{x} + 2 x d x

\frac{2 ^{x}}{ln ( 2 )} + x^{2} + C

求解步骤

\int 2^{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 2^{x} d x + \int 2 x d x

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

\int 2 x d x = x^{2}

= \frac{2 ^{x}}{ln ( 2 )} + x^{2}

解答补常数

= \frac{2 ^{x}}{ln ( 2 )} + x^{2} + C