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人気のある微分積分 >

integral of (-t)/((t+1)-(sqrt(t+1)))

解

\int \frac{- t}{( t + 1 ) - ( t + 1 )} d t

解

- t - 1 - 2 t + 1 + C

解答ステップ

\int \frac{- t}{t + 1 - t + 1} d t

定数を除く:

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

= - \int \frac{t}{t + 1 - t + 1} d t

u置換積分法を適用する

= - \int 2 (u + 1) d u

定数を除く:

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

= - 2 \cdot \int u + 1 d u

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - 2 (\int u d u + \int 1 d u)

\int u d u = \frac{u ^{2}}{2}

\int 1 d u = u

= - 2 (\frac{u ^{2}}{2} + u)

代用を戻す

u = t + 1

= - 2 (\frac{( t + 1 ) ^{2}}{2} + t + 1)

簡素化

- 2 (\frac{( t + 1 ) ^{2}}{2} + t + 1) : - t - 1 - 2 t + 1

= - t - 1 - 2 t + 1

定数を解答に追加する

= - t - 1 - 2 t + 1 + C

グラフ

人気の例

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\frac{\partial}{\partial t} (\frac{3 y ^{2} - t ^{2}}{y ^{5}})

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x \to 0 lim (\frac{( 3 ^{x} - 1 )}{x})

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