integral of 4x^3-9+2sin(x)+7e^x

解答

\int 4 x^{3} - 9 + 2 sin (x) + 7 e^{x} d x

x^{4} - 9 x - 2 cos (x) + 7 e^{x} + C

求解步骤

\int 4 x^{3} - 9 + 2 sin (x) + 7 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 4 x^{3} d x - \int 9 d x + \int 2 sin (x) d x + \int 7 e^{x} d x

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

\int 9 d x = 9 x

\int 2 sin (x) d x = - 2 cos (x)

\int 7 e^{x} d x = 7 e^{x}

= x^{4} - 9 x - 2 cos (x) + 7 e^{x}

解答补常数

= x^{4} - 9 x - 2 cos (x) + 7 e^{x} + C

\int \frac{2 x + 1}{4 x - 1} d x

\int 4 e^{5 t} sin (3 t) d t

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