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

解答

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

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

求解步骤

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

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

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

\int 5 d x = 5 x

\int 5 e^{x} d x = 5 e^{x}

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

解答补常数

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

\int (\frac{1}{2 x + 1}) d x

t an g e n t f (x) = 3 x^{2} - 1, at x = - 2

\int 5 cos (5 x) - 4 d x

7 y^{^{''}} + 30 y = 0

d er i v a t i v e f (x) = 2 x^{2} - x - 3