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人気のある微分積分 >

integral of sin(22x)cos(15x)

解

\int sin (22 x) cos (15 x) d x

解

\frac{1}{2} (- \frac{1}{37} cos (37 x) - \frac{1}{7} cos (7 x)) + C

解答ステップ

\int sin (22 x) cos (15 x) d x

次の恒等を使用する:

cos (t) sin (s) = \frac{sin ( s + t ) + sin ( s - t )}{2}

= \int \frac{sin ( 22 x + 15 x ) + sin ( 22 x - 15 x )}{2} d x

定数を除く:

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

= \frac{1}{2} \cdot \int sin (22 x + 15 x) + sin (22 x - 15 x) d x

簡素化

= \frac{1}{2} \cdot \int sin (37 x) + sin (7 x) 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

= \frac{1}{2} (\int sin (37 x) d x + \int sin (7 x) d x)

\int sin (37 x) d x = - \frac{1}{37} cos (37 x)

\int sin (7 x) d x = - \frac{1}{7} cos (7 x)

= \frac{1}{2} (- \frac{1}{37} cos (37 x) - \frac{1}{7} cos (7 x))

定数を解答に追加する

= \frac{1}{2} (- \frac{1}{37} cos (37 x) - \frac{1}{7} cos (7 x)) + C

グラフ

人気の例

integral from 1 to e^4 of 1/(x(1+ln(x)))

\int_{1}^{e^{4}} \frac{1}{x ( 1 + ln ( x ) )} d x

integral of y^2*cos(y)

\int y^{2} \cdot cos (y) d y

integral of 5/(2x-2)

\int \frac{5}{2 x - 2} d x

limit as x approaches 1+of x/(ln(x))

x \to 1 + lim (\frac{x}{ln ( x )})

limit as x approaches 3 of x^2+x-5

x \to 3 lim (x^{2} + x - 5)