integral of 3xe-2x

解答

\int 3 x e - 2 x d x

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

求解步骤

\int 3 x e - 2 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 3 x e d x - \int 2 x d x

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

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

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

解答补常数

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

\int \frac{y ^{2} - 2 y + 4}{y ( y - 2 ) ^{2}} d y

y^{^{''''}} - y^{^{''}} = 4 x + 2 x e^{- x}

s l o p e (1.4) (7.1)

\int_{3}^{9} \frac{1}{x ( ln ( x ) ) ^{2}} d x

d er i v a t i v e f (x) = \frac{1 - 4 x}{3 + x}