integral of 7x^9-3x^6+10x^3

解答

\int 7 x^{9} - 3 x^{6} + 10 x^{3} d x

\frac{7 x ^{10}}{10} - \frac{3 x ^{7}}{7} + \frac{5 x ^{4}}{2} + C

求解步骤

\int 7 x^{9} - 3 x^{6} + 10 x^{3} 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 7 x^{9} d x - \int 3 x^{6} d x + \int 10 x^{3} d x

\int 7 x^{9} d x = \frac{7 x ^{10}}{10}

\int 3 x^{6} d x = \frac{3 x ^{7}}{7}

\int 10 x^{3} d x = \frac{5 x ^{4}}{2}

= \frac{7 x ^{10}}{10} - \frac{3 x ^{7}}{7} + \frac{5 x ^{4}}{2}

解答补常数

= \frac{7 x ^{10}}{10} - \frac{3 x ^{7}}{7} + \frac{5 x ^{4}}{2} + C

x \to 0 lim (\frac{e ^{b x} - 1}{x})

x \to + 1 lim (\frac{x}{( x - 1 )})

x \to 0 lim (\frac{x - 6}{x - 2})

\frac{d ^{3}}{d x ^{3}} (1 + x)

\frac{d y}{d x} = 12