integral of (x^{1.4}+7x^{2.5})

解答

\int (x^{1.4} + 7 x^{2.5}) d x

0.41666 \dots x^{2.4} + 2 x^{3.5} + C

求解步骤

\int x^{1.4} + 7 x^{2.5} 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 x^{1.4} d x + \int 7 x^{2.5} d x

\int x^{1.4} d x = 0.41666 \dots x^{2.4}

\int 7 x^{2.5} d x = 2 x^{3.5}

= 0.41666 \dots x^{2.4} + 2 x^{3.5}

解答补常数

= 0.41666 \dots x^{2.4} + 2 x^{3.5} + C

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