integral of (4x^2-5x+1)

解答

\int (4 x^{2} - 5 x + 1) d x

\frac{4 x ^{3}}{3} - \frac{5 x ^{2}}{2} + x + C

求解步骤

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

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

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

\int 1 d x = x

= \frac{4 x ^{3}}{3} - \frac{5 x ^{2}}{2} + x

解答补常数

= \frac{4 x ^{3}}{3} - \frac{5 x ^{2}}{2} + x + C

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