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 (arctan(sqrt(x)))/(x^2)

解

\int \frac{arctan ( x )}{x ^{2}} d x

解

- \frac{arctan ( x )}{x} - \frac{1}{x} - arctan (x) + C

解答ステップ

\int \frac{arctan ( x )}{x ^{2}} d x

u置換積分法を適用する

= \int \frac{2 arctan ( u )}{u ^{3}} d u

定数を除く:

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

= 2 \cdot \int \frac{arctan ( u )}{u ^{3}} d u

部分積分を適用する

= 2 (- \frac{arctan ( u )}{2 u ^{2}} - \int - \frac{1}{2 u ^{2} ( u ^{2} + 1 )} d u)

\int - \frac{1}{2 u ^{2} ( u ^{2} + 1 )} d u = - \frac{1}{2} (- \frac{1}{u} - arctan (u))

= 2 (- \frac{arctan ( u )}{2 u ^{2}} - (- \frac{1}{2} (- \frac{1}{u} - arctan (u))))

代用を戻す

u = x

= 2 (- \frac{arctan ( x )}{2 ( x ) ^{2}} - (- \frac{1}{2} (- \frac{1}{x} - arctan (x))))

簡素化

2 (- \frac{arctan ( x )}{2 ( x ) ^{2}} - (- \frac{1}{2} (- \frac{1}{x} - arctan (x)))) : - \frac{arctan ( x )}{x} - \frac{1}{x} - arctan (x)

= - \frac{arctan ( x )}{x} - \frac{1}{x} - arctan (x)

定数を解答に追加する

= - \frac{arctan ( x )}{x} - \frac{1}{x} - arctan (x) + C

グラフ

人気の例

面積 x=4y^2,x+y=3

a re a x = 4 y^{2}, x + y = 3

integral of (10x)/(81x^4+49)

\int \frac{10 x}{81 x ^{4} + 49} d x

integral of arccos(x)

\int arccos (x) d x

integral of cos^7(5x)\sqrt[5]{sin(5x)}

\int cos^{7} (5 x) 5 sin (5 x) d x

integral from-2 to 2 of (x^3-1)

\int_{- 2}^{2} (x^{3} - 1) d x