integral of e^{2x}-x^2-1

解答

\int e^{2 x} - x^{2} - 1 d x

\frac{1}{2} e^{2 x} - \frac{x ^{3}}{3} - x + C

求解步骤

\int e^{2 x} - 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 e^{2 x} d x - \int x^{2} d x - \int 1 d x

\int e^{2 x} d x = \frac{1}{2} e^{2 x}

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

\int 1 d x = x

= \frac{1}{2} e^{2 x} - \frac{x ^{3}}{3} - x

解答补常数

= \frac{1}{2} e^{2 x} - \frac{x ^{3}}{3} - x + C

\frac{d}{d x} (cos (2 x))

y^{^{'}} = y (x y^{2} + 1)

\int 4 sin^{6} (x) cos^{3} (x) d x

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

t an g e n t f (x) = x^{3} - 6 x^{2} + 12 x - 9