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 9sin^3(xco)s^2x

解

\int 9 sin^{3} (x co) s^{2} x d x

解

- \frac{9 s ^{2}}{co} x cos (co x) + \frac{3 s ^{2}}{co} x cos^{3} (co x) + \frac{6 s ^{2}}{c ^{2} o ^{2}} sin (co x) + \frac{s ^{2}}{c ^{2} o ^{2}} sin^{3} (co x) + C

解答ステップ

\int 9 sin^{3} (x co) s^{2} x d x

定数を除く:

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

= 9 s^{2} \cdot \int sin^{3} (co x) x d x

u置換積分法を適用する

= 9 s^{2} \cdot \int \frac{u sin ^{3} ( u )}{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

= 9 s^{2} \frac{1}{c ^{2} o ^{2}} \cdot \int u sin^{3} (u) d u

部分積分を適用する

= 9 s^{2} \frac{1}{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)

= 9 s^{2} \frac{1}{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 = co x

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

簡素化

9 s^{2} \frac{1}{c ^{2} o ^{2}} (co x (- cos (co x) + \frac{1}{3} cos^{3} (co x)) - (- \frac{2}{3} sin (co x) - \frac{1}{9} sin^{3} (co x))) : - \frac{9 s ^{2}}{co} x cos (co x) + \frac{3 s ^{2}}{co} x cos^{3} (co x) + \frac{6 s ^{2}}{c ^{2} o ^{2}} sin (co x) + \frac{s ^{2}}{c ^{2} o ^{2}} sin^{3} (co x)

= - \frac{9 s ^{2}}{co} x cos (co x) + \frac{3 s ^{2}}{co} x cos^{3} (co x) + \frac{6 s ^{2}}{c ^{2} o ^{2}} sin (co x) + \frac{s ^{2}}{c ^{2} o ^{2}} sin^{3} (co x)

定数を解答に追加する

= - \frac{9 s ^{2}}{co} x cos (co x) + \frac{3 s ^{2}}{co} x cos^{3} (co x) + \frac{6 s ^{2}}{c ^{2} o ^{2}} sin (co x) + \frac{s ^{2}}{c ^{2} o ^{2}} sin^{3} (co x) + C

グラフ

人気の例

derivative (2u^2)/((u^2+u)^3)

d er i v a t i v e \frac{2 u ^{2}}{( u ^{2} + u ) ^{3}}

integral of 1/((3x)^2)

\int \frac{1}{( 3 x ) ^{2}} d x

integral from 0 to 6 of pi(3)^2

\int_{0}^{6} π (3)^{2} d x

integral of-1/n cos(nx)

\int - \frac{1}{n} cos (n x) d x

(\partial)/(\partial y)(xy-5y+x^2+y^2-10x)

\frac{\partial}{\partial y} (x y - 5 y + x^{2} + y^{2} - 10 x)