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人気のある微分積分 >

integral of (x+4)(x+3)^{1/4}

解

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

解

\frac{4}{9} (x + 3)^{\frac{9}{4}} + \frac{4}{5} (x + 3)^{\frac{5}{4}} + C

解答ステップ

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

u置換積分法を適用する

= \int u (u - 1)^{\frac{1}{4}} d u

u置換積分法を適用する

= \int (v + 1) v^{\frac{1}{4}} d v

拡張

(v + 1) v^{\frac{1}{4}} : v^{\frac{5}{4}} + v^{\frac{1}{4}}

= \int v^{\frac{5}{4}} + v^{\frac{1}{4}} d v

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

= \int v^{\frac{5}{4}} d v + \int v^{\frac{1}{4}} d v

\int v^{\frac{5}{4}} d v = \frac{4}{9} v^{\frac{9}{4}}

\int v^{\frac{1}{4}} d v = \frac{4}{5} v^{\frac{5}{4}}

= \frac{4}{9} v^{\frac{9}{4}} + \frac{4}{5} v^{\frac{5}{4}}

代用を戻す

= \frac{4}{9} (x + 4 - 1)^{\frac{9}{4}} + \frac{4}{5} (x + 4 - 1)^{\frac{5}{4}}

簡素化

\frac{4}{9} (x + 4 - 1)^{\frac{9}{4}} + \frac{4}{5} (x + 4 - 1)^{\frac{5}{4}} : \frac{4}{9} (x + 3)^{\frac{9}{4}} + \frac{4}{5} (x + 3)^{\frac{5}{4}}

= \frac{4}{9} (x + 3)^{\frac{9}{4}} + \frac{4}{5} (x + 3)^{\frac{5}{4}}

定数を解答に追加する

= \frac{4}{9} (x + 3)^{\frac{9}{4}} + \frac{4}{5} (x + 3)^{\frac{5}{4}} + C

グラフ

人気の例

(cos(arcsin(x)))^'

(cos (arcsin (x)))^{^{'}}

integral of 7/(sqrt(25-x^2))

\int \frac{7}{25 - x ^{2}} d x

d er i v a t i v e 2 x y

derivative f(x)=x^4+4x^3-48x^2+6

d er i v a t i v e f (x) = x^{4} + 4 x^{3} - 48 x^{2} + 6

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