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 10tan^2(x)sec(x)

解

\int 10 tan^{2} (x) sec (x) d x

解

10 (\frac{1}{2} sec (x) tan (x) - \frac{1}{2} ln ∣ tan (x) + sec (x) ∣) + C

解答ステップ

\int 10 tan^{2} (x) sec (x) d x

定数を除く:

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

= 10 \cdot \int tan^{2} (x) sec (x) d x

三角関数の公式を使用して書き換える

= 10 \cdot \int (- 1 + sec^{2} (x)) sec (x) d x

拡張

(- 1 + sec^{2} (x)) sec (x) : - sec (x) + sec^{3} (x)

= 10 \cdot \int - sec (x) + sec^{3} (x) d x

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

= 10 (- \int sec (x) d x + \int sec^{3} (x) d x)

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

\int sec^{3} (x) d x = \frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣

= 10 (- ln ∣ tan (x) + sec (x) ∣ + \frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣)

簡素化

- ln ∣ tan (x) + sec (x) ∣ + \frac{1}{2} sec (x) tan (x) + \frac{1}{2} ln ∣ tan (x) + sec (x) ∣ : \frac{1}{2} sec (x) tan (x) - \frac{1}{2} ln ∣ tan (x) + sec (x) ∣

= 10 (\frac{1}{2} sec (x) tan (x) - \frac{1}{2} ln ∣ tan (x) + sec (x) ∣)

定数を解答に追加する

= 10 (\frac{1}{2} sec (x) tan (x) - \frac{1}{2} ln ∣ tan (x) + sec (x) ∣) + C

グラフ

人気の例

integral of (-1)/((1+x)^2)

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

integral of e^{a*x}

\int e^{a \cdot x} d x

integral of (t+5)^2sqrt(3-t)

\int (t + 5)^{2} 3 - t d t

integral of 4cos(t)sin(t)

\int 4 cos (t) sin (t) d t

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

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