integral of (3+2/5 x^2+3/7 x^3)

解答

\int (3 + \frac{2}{5} x^{2} + \frac{3}{7} x^{3}) d x

3 x + \frac{2 x ^{3}}{15} + \frac{3 x ^{4}}{28} + C

求解步骤

\int 3 + \frac{2}{5} x^{2} + \frac{3}{7} 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 3 d x + \int \frac{2}{5} x^{2} d x + \int \frac{3}{7} x^{3} d x

\int 3 d x = 3 x

\int \frac{2}{5} x^{2} d x = \frac{2 x ^{3}}{15}

\int \frac{3}{7} x^{3} d x = \frac{3 x ^{4}}{28}

= 3 x + \frac{2 x ^{3}}{15} + \frac{3 x ^{4}}{28}

解答补常数

= 3 x + \frac{2 x ^{3}}{15} + \frac{3 x ^{4}}{28} + C

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