ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

integral of sin(7x)cos(5x)

解

\int sin (7 x) cos (5 x) d x

解

\frac{1}{2} (- \frac{1}{12} cos (12 x) - \frac{1}{2} cos (2 x)) + C

解答ステップ

\int sin (7 x) cos (5 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 ( 7 x + 5 x ) + sin ( 7 x - 5 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 (7 x + 5 x) + sin (7 x - 5 x) d x

簡素化

= \frac{1}{2} \cdot \int sin (12 x) + sin (2 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 (12 x) d x + \int sin (2 x) d x)

\int sin (12 x) d x = - \frac{1}{12} cos (12 x)

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

= \frac{1}{2} (- \frac{1}{12} cos (12 x) - \frac{1}{2} cos (2 x))

定数を解答に追加する

= \frac{1}{2} (- \frac{1}{12} cos (12 x) - \frac{1}{2} cos (2 x)) + C

グラフ

人気の例

limit as h approaches 0 of (3e^h-3)/h

h \to 0 lim (\frac{3 e ^{h} - 3}{h})

integral from-infinity to 0 of x/(x^4+4)

\int_{- \infty}^{0} \frac{x}{x ^{4} + 4} d x

integral of 2/(sqrt(4x^2+4))

\int \frac{2}{4 x ^{2} + 4} d x

integral from ln(3) to ln(5) of e^{2x}

\int_{l n (3)}^{l n (5)} e^{2 x} d x

tangent f(x)=3^x,\at x=0

t an g e n t f (x) = 3^{x}, at x = 0