integral of 2x^7+4x^6+x^5+1

解答

\int 2 x^{7} + 4 x^{6} + x^{5} + 1 d x

\frac{x ^{8}}{4} + \frac{4 x ^{7}}{7} + \frac{x ^{6}}{6} + x + C

求解步骤

\int 2 x^{7} + 4 x^{6} + x^{5} + 1 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^{7} d x + \int 4 x^{6} d x + \int x^{5} d x + \int 1 d x

\int 2 x^{7} d x = \frac{x ^{8}}{4}

\int 4 x^{6} d x = \frac{4 x ^{7}}{7}

\int x^{5} d x = \frac{x ^{6}}{6}

\int 1 d x = x

= \frac{x ^{8}}{4} + \frac{4 x ^{7}}{7} + \frac{x ^{6}}{6} + x

解答补常数

= \frac{x ^{8}}{4} + \frac{4 x ^{7}}{7} + \frac{x ^{6}}{6} + x + C

t an g e n t y = 2 x^{3} - 2 x, (- 1, 0)

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