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人気のある微分積分 >

integral of 6/((x-4)(x+2))

解

\int \frac{6}{( x - 4 ) ( x + 2 )} d x

解

ln ∣ x - 4 ∣ - ln ∣ x + 2 ∣ + C

解答ステップ

\int \frac{6}{( x - 4 ) ( x + 2 )} d x

定数を除く:

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

= 6 \cdot \int \frac{1}{( x - 4 ) ( x + 2 )} d x

以下の部分分数を得る:

\frac{1}{( x - 4 ) ( x + 2 )} : \frac{1}{6 ( x - 4 )} - \frac{1}{6 ( x + 2 )}

= 6 \cdot \int \frac{1}{6 ( x - 4 )} - \frac{1}{6 ( x + 2 )} d x

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

= 6 (\int \frac{1}{6 ( x - 4 )} d x - \int \frac{1}{6 ( x + 2 )} d x)

\int \frac{1}{6 ( x - 4 )} d x = \frac{1}{6} ln ∣ x - 4 ∣

\int \frac{1}{6 ( x + 2 )} d x = \frac{1}{6} ln ∣ x + 2 ∣

= 6 (\frac{1}{6} ln ∣ x - 4 ∣ - \frac{1}{6} ln ∣ x + 2 ∣)

簡素化

6 (\frac{1}{6} ln ∣ x - 4 ∣ - \frac{1}{6} ln ∣ x + 2 ∣) : ln ∣ x - 4 ∣ - ln ∣ x + 2 ∣

= ln ∣ x - 4 ∣ - ln ∣ x + 2 ∣

定数を解答に追加する

= ln ∣ x - 4 ∣ - ln ∣ x + 2 ∣ + C

グラフ

人気の例

y^{''}+81y=sec^2(9x)

y^{^{''}} + 81 y = sec^{2} (9 x)

勾配 (1/4 , 7/8),(4 1/4 ,2 7/8)

s l o p e (\frac{1}{4}, \frac{7}{8}), (4 \frac{1}{4}, 2 \frac{7}{8})

sum from n=0 to infinity of 1/((2n+1)^6)

n = 0 \sum \infty \frac{1}{( 2 n + 1 ) ^{6}}

sqrt(y)dx+(1+x)dy=0

y d x + (1 + x) d y = 0

(\partial)/(\partial x)((x^2+y^2-7)/(xy))

\frac{\partial}{\partial x} (\frac{x ^{2} + y ^{2} - 7}{x y})