ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

integral of xe^{sqrt(x)}

解

\int x e^{x} d x

解

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

解答ステップ

\int x e^{x} d x

u置換積分法を適用する

= \int 2 e^{u} u^{3} d u

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int e^{u} u^{3} d u

部分積分を適用する

= 2 (u^{3} e^{u} - \int 3 u^{2} e^{u} d u)

\int 3 u^{2} e^{u} d u = 3 (u^{2} e^{u} - 2 (e^{u} u - e^{u}))

= 2 (u^{3} e^{u} - 3 (u^{2} e^{u} - 2 (e^{u} u - e^{u})))

代用を戻す

u = x

= 2 ((x)^{3} e^{x} - 3 ((x)^{2} e^{x} - 2 (e^{x} x - e^{x})))

簡素化

2 ((x)^{3} e^{x} - 3 ((x)^{2} e^{x} - 2 (e^{x} x - e^{x}))) : 2 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x})))

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

定数を解答に追加する

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

グラフ

人気の例

integral from 0 to 1 of (e^z+1)/(e^z+z)

\int_{0}^{1} \frac{e ^{z} + 1}{e ^{z} + z} d z

(dy)/(dx)=40-3y

\frac{d y}{d x} = 40 - 3 y

integral of x^3cos(x^4+1)

\int x^{3} cos (x^{4} + 1) d x

integral of (6+x^9)^5x^8

\int (6 + x^{9})^{5} x^{8} d x

limit as h approaches infinity of (3h+2xh^2+x^2+h^3)/(4-3xh-2x^3h^3)

h \to \infty lim (\frac{3 h + 2 x h ^{2} + x ^{2} + h ^{3}}{4 - 3 x h - 2 x ^{3} h ^{3}})