integral of-2x^5-5x^3+3x^2+1-4e^x

解答

\int - 2 x^{5} - 5 x^{3} + 3 x^{2} + 1 - 4 e^{x} d x

- \frac{x ^{6}}{3} - \frac{5 x ^{4}}{4} + x^{3} + x - 4 e^{x} + C

求解步骤

\int - 2 x^{5} - 5 x^{3} + 3 x^{2} + 1 - 4 e^{x} 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 2 x^{5} d x - \int 5 x^{3} d x + \int 3 x^{2} d x + \int 1 d x - \int 4 e^{x} d x

\int 2 x^{5} d x = \frac{x ^{6}}{3}

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

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

\int 1 d x = x

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

= - \frac{x ^{6}}{3} - \frac{5 x ^{4}}{4} + x^{3} + x - 4 e^{x}

解答补常数

= - \frac{x ^{6}}{3} - \frac{5 x ^{4}}{4} + x^{3} + x - 4 e^{x} + C

\int_{2}^{3} \frac{2}{t ^{2} - 1} d t

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