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人気のある微分積分 >

integral of (13(tan(x))^2)/(sec(x))

解

\int \frac{13 ( tan ( x ) ) ^{2}}{sec ( x )} d x

解

13 (ln ∣ tan (x) + sec (x) ∣ - sin (x)) + C

解答ステップ

\int \frac{13 ( tan ( x ) ) ^{2}}{sec ( x )} d x

定数を除く:

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

= 13 \cdot \int \frac{( tan ( x ) ) ^{2}}{sec ( x )} d x

簡素化

\frac{( tan ( x ) ) ^{2}}{sec ( x )} : sin (x) tan (x)

= 13 \cdot \int sin (x) tan (x) d x

三角関数の公式を使用して書き換える

= 13 \cdot \int \frac{1 - cos ^{2} ( x )}{cos ( x )} d x

拡張

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

= 13 \cdot \int \frac{1}{cos ( x )} - cos (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

= 13 (\int \frac{1}{cos ( x )} d x - \int cos (x) d x)

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

\int cos (x) d x = sin (x)

= 13 (ln ∣ tan (x) + sec (x) ∣ - sin (x))

定数を解答に追加する

= 13 (ln ∣ tan (x) + sec (x) ∣ - sin (x)) + C

グラフ

人気の例

積分記号 e^{y^2}

in t e g r a l e^{y^{2}}

integral of 11/4 cos(7/8 x+23)

\int \frac{11}{4} cos (\frac{7}{8} x + 23) d x

integral of (x^3)/(2-3x^4)

\int \frac{x ^{3}}{2 - 3 x ^{4}} d x

integral of (170)/((x+1)(x^2+9)^2)

\int \frac{170}{( x + 1 ) ( x ^{2} + 9 ) ^{2}} d x

integral of 2/(4-x)

\int \frac{2}{4 - x} d x