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人気のある微分積分 >

integral of (cos(x)-(sin(x))/x)/(x)

解

\int \frac{cos ( x ) - \frac{s i n ( x )}{x}}{x} d x

解

\frac{sin ( x )}{x} + C

解答ステップ

\int \frac{cos ( x ) - \frac{s i n ( x )}{x}}{x} d x

簡素化

\frac{cos ( x ) - \frac{s i n ( x )}{x}}{x} : \frac{x cos ( x ) - sin ( x )}{x ^{2}}

= \int \frac{x cos ( x ) - sin ( x )}{x ^{2}} d x

拡張

\frac{x cos ( x ) - sin ( x )}{x ^{2}} : \frac{cos ( x )}{x} - \frac{sin ( x )}{x ^{2}}

= \int \frac{cos ( x )}{x} - \frac{sin ( x )}{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 \frac{cos ( x )}{x} d x - \int \frac{sin ( x )}{x ^{2}} d x

\int \frac{cos ( x )}{x} d x = Ci (x)

\int \frac{sin ( x )}{x ^{2}} d x = - \frac{sin ( x )}{x} + Ci (x)

= Ci (x) - (- \frac{sin ( x )}{x} + Ci (x))

簡素化

= \frac{sin ( x )}{x}

定数を解答に追加する

= \frac{sin ( x )}{x} + C

グラフ

人気の例

(\partial)/(\partial x)(-2xy(6-x-y))

\frac{\partial}{\partial x} (- 2 x y (6 - x - y))

limit as x approaches 0 of log_{3}(x)

x \to 0 lim (lo g_{3} (x))

derivative sqrt(4x+1)

d er i v a t i v e 4 x + 1

integral of (2x-3)/((x^2-3x+6)^2)

\int \frac{2 x - 3}{( x ^{2} - 3 x + 6 ) ^{2}} d x

limit as x approaches 4 of x/(x^2+4)

x \to 4 lim (\frac{x}{x ^{2} + 4})