integral of 9x^2-34x+25

解答

\int 9 x^{2} - 34 x + 25 d x

3 x^{3} - 17 x^{2} + 25 x + C

求解步骤

\int 9 x^{2} - 34 x + 25 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 9 x^{2} d x - \int 34 x d x + \int 25 d x

\int 9 x^{2} d x = 3 x^{3}

\int 34 x d x = 17 x^{2}

\int 25 d x = 25 x

= 3 x^{3} - 17 x^{2} + 25 x

解答补常数

= 3 x^{3} - 17 x^{2} + 25 x + C

\int x^{3} - 4 x^{2} + x + 6 d x

\int x^{\frac{1}{2}} \cdot ln (x) d x

\int (x - 3) sin (x) d x

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

\int \frac{1 + 4 ln ( x )}{x} d x