integral of 6x^2+1

解答

\int 6 x^{2} + 1 d x

2 x^{3} + x + C

求解步骤

\int 6 x^{2} + 1 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 6 x^{2} d x + \int 1 d x

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

\int 1 d x = x

= 2 x^{3} + x

解答补常数

= 2 x^{3} + x + C

x \to 0 + lim (- \frac{1}{x ^{2}})

y^{^{''}} - 5 y^{^{'}} + 9 y = x e^{x}

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

\int tan^{5} (x) d x

(x + y) e^{\frac{x}{y}} d x + (x - \frac{x ^{2}}{y}) e^{\frac{x}{y}} d y = 0