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人気のある微分積分 >

integral of-sin(x)sec(x)tan(x)

解

\int - sin (x) sec (x) tan (x) d x

解

- tan (x) + x + C

解答ステップ

\int - sin (x) sec (x) tan (x) d x

定数を除く:

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

= - \int sin (x) sec (x) tan (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 ^{2} ( x )} d x

拡張

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

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

\int \frac{1}{cos ^{2} ( x )} d x = tan (x)

\int 1 d x = x

= - (tan (x) - x)

簡素化

= - tan (x) + x

定数を解答に追加する

= - tan (x) + x + C

グラフ

人気の例

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

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

derivative sqrt(3-9x)

d er i v a t i v e 3 - 9 x

derivative of 4x-3/x+1/(x^2)

\frac{d}{d x} (4 x - \frac{3}{x} + \frac{1}{x ^{2}})

integral of ln(x)(sqrt(1-(ln(x))^2))/x

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

integral of 1/(sqrt(2x))cos(sqrt(2x))

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