integral of 3x^2-sqrt(5x)+2

解答

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

x^{3} - 5 \frac{2}{3} x^{\frac{3}{2}} + 2 x + C

求解步骤

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

使用根式运算法则:

n ab = n a n b,

假定

a \geq 0, b \geq 0

= \int 3 x^{2} - 5 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 3 x^{2} d x - \int 5 x d x + \int 2 d x

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

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

\int 2 d x = 2 x

= x^{3} - 5 \frac{2}{3} x^{\frac{3}{2}} + 2 x

解答补常数

= x^{3} - 5 \frac{2}{3} x^{\frac{3}{2}} + 2 x + C

\int_{0}^{\infty} 6 e^{- 3 x} d x

\frac{d}{d x} (\frac{x - 19}{x - 19})

t an g e n t f (x) = x^{4} - 13 x^{2} + 36, at x = 1

l a pl a ce t r an s f or m (25 t) ((\frac{t}{25})^{2})

\frac{d}{d x} (x^{2} + \frac{1}{2 x} - 3 x)