integral of sin(0.01t)+t^3

解答

\int sin (0.01 t) + t^{3} d t

- 100 cos (0.01 t) + 0.25 t^{4} + C

求解步骤

\int sin (0.01 t) + t^{3} 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 sin (0.01 t) d t + \int t^{3} d t

\int sin (0.01 t) d t = - 100 cos (0.01 t)

\int t^{3} d t = \frac{t ^{4}}{4}

= - 100 cos (0.01 t) + \frac{t ^{4}}{4}

化简

= - 100 cos (0.01 t) + 0.25 t^{4}

解答补常数

= - 100 cos (0.01 t) + 0.25 t^{4} + C

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