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人気のある微分積分 >

integral of-(sin^2(x))/(cos(x))

解

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

解

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

解答ステップ

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

定数を除く:

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

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

三角関数の公式を使用して書き換える

= - \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)

= - \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

= - (\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)

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

簡素化

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

定数を解答に追加する

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

グラフ

人気の例

derivative of (x^2+3/(x^2-1))

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

derivative (sin(4t))/(cos(6t))

d er i v a t i v e \frac{sin ( 4 t )}{cos ( 6 t )}

derivative y=sqrt(x)^{3x}

d er i v a t i v e y = x^{3 x}

y^{''}+y=sec(t)

y^{^{''}} + y = sec (t)

sum from n=1 to infinity of (6n)/(9-2n)

n = 1 \sum \infty \frac{6 n}{9 - 2 n}