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受欢迎的微积分 >

integral of sec^7(4x)tan(4x)

解答

\int sec^{7} (4 x) tan (4 x) d x

解答

\frac{1}{28} sec^{7} (4 x) + C

求解步骤

\int sec^{7} (4 x) tan (4 x) d x

使用换元积分法

= \int sec^{7} (u) tan (u) \frac{1}{4} d u

提出常数:

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

= \frac{1}{4} \cdot \int sec^{7} (u) tan (u) d u

使用换元积分法

= \frac{1}{4} \cdot \int v^{6} d v

使用幂法则

= \frac{1}{4} \cdot \frac{v ^{7}}{7}

代回

= \frac{1}{4} \cdot \frac{sec ^{7} ( 4 x )}{7}

化简

\frac{1}{4} \cdot \frac{sec ^{7} ( 4 x )}{7} : \frac{1}{28} sec^{7} (4 x)

= \frac{1}{28} sec^{7} (4 x)

解答补常数

= \frac{1}{28} sec^{7} (4 x) + C

作图

流行的例子

derivative of 524288sin(2x)

\frac{d}{d x} (524288 sin (2 x))

derivative 1/(2x^4)

d er i v a t i v e \frac{1}{2 x ^{4}}

integral from 2 to 3 of (37)/(sqrt(3-x))

\int_{2}^{3} \frac{37}{3 - x} d x

integral of 7x^{2/5}+5x^{-4/5}

\int 7 x^{\frac{2}{5}} + 5 x^{- \frac{4}{5}} d x

斜率 (0,4),(2,-3)

s l o p e (0, 4), (2, - 3)