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 cos^4(6x)

解

\int cos^{4} (6 x) d x

解

\frac{1}{6} (cos^{3} (6 x) sin (6 x) + \frac{3}{8} (6 x - \frac{1}{4} sin (24 x))) + C

解答ステップ

\int cos^{4} (6 x) d x

u置換積分法を適用する

= \int cos^{4} (u) \frac{1}{6} d u

定数を除く:

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

= \frac{1}{6} \cdot \int cos^{4} (u) d u

簡素化

cos^{4} (u) : cos^{3} (u) cos (u)

= \frac{1}{6} \cdot \int cos^{3} (u) cos (u) d u

部分積分を適用する

= \frac{1}{6} (cos^{3} (u) sin (u) - \int - 3 cos^{2} (u) sin^{2} (u) d u)

\int - 3 cos^{2} (u) sin^{2} (u) d u = - \frac{3}{8} (u - \frac{1}{4} sin (4 u))

= \frac{1}{6} (cos^{3} (u) sin (u) - (- \frac{3}{8} (u - \frac{1}{4} sin (4 u))))

代用を戻す

u = 6 x

= \frac{1}{6} (cos^{3} (6 x) sin (6 x) - (- \frac{3}{8} (6 x - \frac{1}{4} sin (4 \cdot 6 x))))

簡素化

= \frac{1}{6} (cos^{3} (6 x) sin (6 x) + \frac{3}{8} (6 x - \frac{1}{4} sin (24 x)))

定数を解答に追加する

= \frac{1}{6} (cos^{3} (6 x) sin (6 x) + \frac{3}{8} (6 x - \frac{1}{4} sin (24 x))) + C

グラフ

人気の例

derivative of 1/e e^x

\frac{d}{d x} (\frac{1}{e} e^{x})

derivative 1/x+1/(x-1)+1/(x-2)

d er i v a t i v e \frac{1}{x} + \frac{1}{x - 1} + \frac{1}{x - 2}

integral of x^2*sin(x^3)

\int x^{2} \cdot sin (x^{3}) d x

sum from n=1 to infinity of 15(1/100)^n

n = 1 \sum \infty 15 (\frac{1}{100})^{n}

derivative of (x^2/2+1/x)

\frac{d}{d x} (\frac{x ^{2}}{2} + \frac{1}{x})