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 (1+cos(2x))/(sin^2(2x))

解

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

解

\frac{1}{2} (- cot (2 x) - csc (2 x)) + C

解答ステップ

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

u置換積分法を適用する

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

定数を除く:

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

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

拡張

\frac{1 + cos ( u )}{sin ^{2} ( u )} : \frac{1}{sin ^{2} ( u )} + \frac{cos ( u )}{sin ^{2} ( u )}

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

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 \frac{1}{sin ^{2} ( u )} d u + \int \frac{cos ( u )}{sin ^{2} ( u )} d u)

\int \frac{1}{sin ^{2} ( u )} d u = - cot (u)

\int \frac{cos ( u )}{sin ^{2} ( u )} d u = - csc (u)

= \frac{1}{2} (- cot (u) - csc (u))

代用を戻す

u = 2 x

= \frac{1}{2} (- cot (2 x) - csc (2 x))

定数を解答に追加する

= \frac{1}{2} (- cot (2 x) - csc (2 x)) + C

グラフ

人気の例

(\partial)/(\partial y)(x+3y)

勾配 (-1.3)(3.5)

derivative g(x)=ln^3(x)

tangent y=(5x)/(2^x),\at x=2

(\partial)/(\partial y)(ln(x^2+3y))