integral of 3-2t+t^2

解答

\int 3 - 2 t + t^{2} d t

3 t - t^{2} + \frac{t ^{3}}{3} + C

求解步骤

\int 3 - 2 t + t^{2} d t

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 t - \int 2 t d t + \int t^{2} d t

\int 3 d t = 3 t

\int 2 t d t = t^{2}

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

= 3 t - t^{2} + \frac{t ^{3}}{3}

解答补常数

= 3 t - t^{2} + \frac{t ^{3}}{3} + C

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