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 5sin^3(5xco)s^35x

解

\int 5 sin^{3} (5 x co) s^{3} 5 x d x

解

s^{3} \frac{1}{c ^{2} o ^{2}} (- 5 co x cos (5 co x) + \frac{5}{3} co x cos^{3} (5 co x) + \frac{2}{3} sin (5 co x) + \frac{1}{9} sin^{3} (5 co x)) + C

解答ステップ

\int 5 sin^{3} (5 x co) s^{3} \cdot 5 x d x

定数を除く:

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

= 5 \cdot 5 s^{3} \cdot \int sin^{3} (5 co x) x d x

簡素化

= 25 s^{3} \cdot \int sin^{3} (5 co x) x d x

u置換積分法を適用する

= 25 s^{3} \cdot \int \frac{u sin ^{3} ( u )}{25 c ^{2} o ^{2}} d u

定数を除く:

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

= 25 s^{3} \frac{1}{25 c ^{2} o ^{2}} \cdot \int u sin^{3} (u) d u

部分積分を適用する

= 25 s^{3} \frac{1}{25 c ^{2} o ^{2}} (u (- cos (u) + \frac{1}{3} cos^{3} (u)) - \int - cos (u) + \frac{1}{3} cos^{3} (u) d u)

\int - cos (u) + \frac{1}{3} cos^{3} (u) d u = - \frac{2}{3} sin (u) - \frac{1}{9} sin^{3} (u)

= 25 s^{3} \frac{1}{25 c ^{2} o ^{2}} (u (- cos (u) + \frac{1}{3} cos^{3} (u)) - (- \frac{2}{3} sin (u) - \frac{1}{9} sin^{3} (u)))

代用を戻す

u = 5 co x

= 25 s^{3} \frac{1}{25 c ^{2} o ^{2}} (5 co x (- cos (5 co x) + \frac{1}{3} cos^{3} (5 co x)) - (- \frac{2}{3} sin (5 co x) - \frac{1}{9} sin^{3} (5 co x)))

簡素化

25 s^{3} \frac{1}{25 c ^{2} o ^{2}} (5 co x (- cos (5 co x) + \frac{1}{3} cos^{3} (5 co x)) - (- \frac{2}{3} sin (5 co x) - \frac{1}{9} sin^{3} (5 co x))) : s^{3} \frac{1}{c ^{2} o ^{2}} (- 5 co x cos (5 co x) + \frac{5}{3} co x cos^{3} (5 co x) + \frac{2}{3} sin (5 co x) + \frac{1}{9} sin^{3} (5 co x))

= s^{3} \frac{1}{c ^{2} o ^{2}} (- 5 co x cos (5 co x) + \frac{5}{3} co x cos^{3} (5 co x) + \frac{2}{3} sin (5 co x) + \frac{1}{9} sin^{3} (5 co x))

定数を解答に追加する

= s^{3} \frac{1}{c ^{2} o ^{2}} (- 5 co x cos (5 co x) + \frac{5}{3} co x cos^{3} (5 co x) + \frac{2}{3} sin (5 co x) + \frac{1}{9} sin^{3} (5 co x)) + C

グラフ

人気の例

integral from 9 to 10 of 1/((x-9)^{5/4)}

\int_{9}^{10} \frac{1}{( x - 9 ) ^{\frac{5}{4}}} d x

derivative of x/2-tan(x)

\frac{d}{d x} (\frac{x}{2} - tan (x))

integral of sec(x)tan^3(x)

\int sec (x) tan^{3} (x) d x

limit as x approaches 3 of-x+2

x \to 3 lim (- x + 2)

integral of (x^5)/((x^2+4)^2)

\int \frac{x ^{5}}{( x ^{2} + 4 ) ^{2}} d x