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人気のある微分積分 >

integral of (e^{1/t})/(t^3)

解

\int \frac{e ^{\frac{1}{t}}}{t ^{3}} d t

解

- \frac{e ^{\frac{1}{t}}}{t} + e^{\frac{1}{t}} + C

解答ステップ

\int \frac{e ^{\frac{1}{t}}}{t ^{3}} d t

u置換積分法を適用する

= \int - e^{u} u d u

定数を除く:

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

= - \int e^{u} u d u

部分積分を適用する

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

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

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

代用を戻す

u = \frac{1}{t}

= - (e^{\frac{1}{t}} \frac{1}{t} - e^{\frac{1}{t}})

簡素化

- (e^{\frac{1}{t}} \frac{1}{t} - e^{\frac{1}{t}}) : - \frac{e ^{\frac{1}{t}}}{t} + e^{\frac{1}{t}}

= - \frac{e ^{\frac{1}{t}}}{t} + e^{\frac{1}{t}}

定数を解答に追加する

= - \frac{e ^{\frac{1}{t}}}{t} + e^{\frac{1}{t}} + C

グラフ

人気の例

d er i v a t i v e e^{y}

integral of cos(x)(2+sin(x))^5

\int cos (x) (2 + sin (x))^{5} d x

limit as x approaches 0 of x^2+2x-2

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

(\partial)/(\partial x)(e^xln(1+y))

\frac{\partial}{\partial x} (e^{x} ln (1 + y))

(x+1)(dy)/(dx)+y=ln(x),y(1)=10

(x + 1) \frac{d y}{d x} + y = ln (x), y (1) = 10