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人気のある微分積分 >

integral of (3x+5)^2((7x-4)/(x^2))

解

\int (3 x + 5)^{2} (\frac{7 x - 4}{x ^{2}}) d x

解

\frac{63 x ^{2}}{2} + 174 x + 55 ln ∣ x ∣ + \frac{100}{x} + C

解答ステップ

\int (3 x + 5)^{2} \frac{7 x - 4}{x ^{2}} d x

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \int \frac{( 7 x - 4 ) ( 3 x + 5 ) ^{2}}{x ^{2}} d x

拡張

\frac{( 7 x - 4 ) ( 3 x + 5 ) ^{2}}{x ^{2}} : 63 x + 174 + \frac{55}{x} - \frac{100}{x ^{2}}

= \int 63 x + 174 + \frac{55}{x} - \frac{100}{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

= \int 63 x d x + \int 174 d x + \int \frac{55}{x} d x - \int \frac{100}{x ^{2}} d x

\int 63 x d x = \frac{63 x ^{2}}{2}

\int 174 d x = 174 x

\int \frac{55}{x} d x = 55 ln ∣ x ∣

\int \frac{100}{x ^{2}} d x = - \frac{100}{x}

= \frac{63 x ^{2}}{2} + 174 x + 55 ln ∣ x ∣ - (- \frac{100}{x})

簡素化

= \frac{63 x ^{2}}{2} + 174 x + 55 ln ∣ x ∣ + \frac{100}{x}

定数を解答に追加する

= \frac{63 x ^{2}}{2} + 174 x + 55 ln ∣ x ∣ + \frac{100}{x} + C

グラフ

人気の例

limit as x approaches+0 of-7/(1-7x)

x \to + 0 lim (- \frac{7}{1 - 7 x})

derivative f(x)=7x-3

d er i v a t i v e f (x) = 7 x - 3

implicit (dy)/(dx),5x^2+3xy-y^2=2

im pl i c i t \frac{d y}{d x}, 5 x^{2} + 3 x y - y^{2} = 2

derivative of x^{2cos(x})

\frac{d}{d x} (x^{2 c o s (x)})

テイラー x/(1+x)

t a y l or \frac{x}{1 + x}