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人気のある微分積分 >

integral of sin(1-2x)cos(1+2x)

解

\int sin (1 - 2 x) cos (1 + 2 x) d x

解

\frac{1}{2} (sin (2) x + \frac{1}{4} cos (4 x)) + C

解答ステップ

\int sin (1 - 2 x) cos (1 + 2 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 ( 1 - 2 x + 1 + 2 x ) + sin ( 1 - 2 x - ( 1 + 2 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 (1 - 2 x + 1 + 2 x) + sin (1 - 2 x - (1 + 2 x)) d x

簡素化

sin (1 - 2 x + 1 + 2 x) + sin (1 - 2 x - (1 + 2 x)) : sin (2) - sin (4 x)

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

\int sin (2) d x = sin (2) x

\int sin (4 x) d x = - \frac{1}{4} cos (4 x)

= \frac{1}{2} (sin (2) x - (- \frac{1}{4} cos (4 x)))

簡素化

= \frac{1}{2} (sin (2) x + \frac{1}{4} cos (4 x))

定数を解答に追加する

= \frac{1}{2} (sin (2) x + \frac{1}{4} cos (4 x)) + C

グラフ

人気の例

derivative of (8x^2-5x(13x^2+4))

\frac{d}{d x} ((8 x^{2} - 5 x) (13 x^{2} + 4))

(\partial)/(\partial x)(ce^{-x}sin(4x))

\frac{\partial}{\partial x} (c e^{- x} sin (4 x))

integral of 3te^t

\int 3 t e^{t} d t

integral of (x^2)/(sqrt(x^3+3))

\int \frac{x ^{2}}{x ^{3} + 3} d x

integral of (sin(x))^2

\int (sin (x))^{2} d x