integral of (2x^{4/3}+3x-1)

解答

\int (2 x^{\frac{4}{3}} + 3 x - 1) d x

\frac{6}{7} x^{\frac{7}{3}} + \frac{3 x ^{2}}{2} - x + C

求解步骤

\int 2 x^{\frac{4}{3}} + 3 x - 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^{\frac{4}{3}} d x + \int 3 x d x - \int 1 d x

\int 2 x^{\frac{4}{3}} d x = \frac{6}{7} x^{\frac{7}{3}}

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

\int 1 d x = x

= \frac{6}{7} x^{\frac{7}{3}} + \frac{3 x ^{2}}{2} - x

解答补常数

= \frac{6}{7} x^{\frac{7}{3}} + \frac{3 x ^{2}}{2} - x + C

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