integral of 4x^3+2x+1

解答

\int 4 x^{3} + 2 x + 1 d x

x^{4} + x^{2} + x + C

求解步骤

\int 4 x^{3} + 2 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^{3} d x + \int 2 x d x + \int 1 d x

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

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

\int 1 d x = x

= x^{4} + x^{2} + x

解答补常数

= x^{4} + x^{2} + x + C

\int \frac{1}{a} e^{- \frac{x}{a}} d x

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