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人気のある微分積分 >

integral of sec^9(x)tan^3(x)

解

\int sec^{9} (x) tan^{3} (x) d x

解

\frac{sec ^{11} ( x )}{11} - \frac{sec ^{9} ( x )}{9} + C

解答ステップ

\int sec^{9} (x) tan^{3} (x) d x

三角関数の公式を使用して書き換える

= \int (- 1 + sec^{2} (x)) tan (x) sec^{9} (x) d x

u置換積分法を適用する

= \int u^{8} (u^{2} - 1) d u

拡張

u^{8} (u^{2} - 1) : u^{10} - u^{8}

= \int u^{10} - u^{8} d u

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 u^{10} d u - \int u^{8} d u

\int u^{10} d u = \frac{u ^{11}}{11}

\int u^{8} d u = \frac{u ^{9}}{9}

= \frac{u ^{11}}{11} - \frac{u ^{9}}{9}

代用を戻す

u = sec (x)

= \frac{sec ^{11} ( x )}{11} - \frac{sec ^{9} ( x )}{9}

定数を解答に追加する

= \frac{sec ^{11} ( x )}{11} - \frac{sec ^{9} ( x )}{9} + C

グラフ

人気の例

integral from 0 to pi/4 of xsec^2(x)

\int_{0}^{\frac{π}{4}} x sec^{2} (x) d x

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d er i v a t i v e f (x) = \frac{- 4}{x}

sum from n=1 to infinity of ((2pi)/3)^n

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

integral of xcos^2(5x)

\int x cos^{2} (5 x) d x