integral of (2+x)^2

解答

\int (2 + x)^{2} d x

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

求解步骤

\int (2 + x)^{2} d x

乘开

(2 + x)^{2} : 4 + 4 x + x^{2}

= \int 4 + 4 x + x^{2} 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 d x + \int 4 x d x + \int x^{2} d x

\int 4 d x = 4 x

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

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

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

解答补常数

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

\int (3 x^{2} - sec^{2} (x)) d x

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