integral of (10x^6+5x^2+4x-7)

解答

\int (10 x^{6} + 5 x^{2} + 4 x - 7) d x

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

求解步骤

\int 10 x^{6} + 5 x^{2} + 4 x - 7 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 10 x^{6} d x + \int 5 x^{2} d x + \int 4 x d x - \int 7 d x

\int 10 x^{6} d x = \frac{10 x ^{7}}{7}

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

\int 4 x d x = 2 x^{2}

\int 7 d x = 7 x

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

解答补常数

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

\int \frac{x ^{3} - 2}{3 x - 3} d x

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