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受欢迎的微积分 >

integral of sec^2(x)tan(x)e^{sec(x)}

解答

\int sec^{2} (x) tan (x) e^{s e c (x)} d x

解答

- e^{s e c (x)} + e^{s e c (x)} ln (e^{s e c (x)}) + C

求解步骤

\int sec^{2} (x) tan (x) e^{s e c (x)} d x

使用换元积分法

= \int e^{1 + u^{2}} u d u

使用换元积分法

= \int ln (v) d v

使用分布积分法

= v ln (v) - \int 1 d v

\int 1 d v = v

= v ln (v) - v

代回

= e^{1 + t a n^{2} (x)} ln (e^{1 + t a n^{2} (x)}) - e^{1 + t a n^{2} (x)}

化简

e^{1 + t a n^{2} (x)} ln (e^{1 + t a n^{2} (x)}) - e^{1 + t a n^{2} (x)} : - e^{s e c (x)} + e^{s e c (x)} ln (e^{s e c (x)})

= - e^{s e c (x)} + e^{s e c (x)} ln (e^{s e c (x)})

解答补常数

= - e^{s e c (x)} + e^{s e c (x)} ln (e^{s e c (x)}) + C

作图

流行的例子

derivative sin(cos(5x))

d er i v a t i v e sin (cos (5 x))

integral of sin(x)+8

\int sin (x) + 8 d x

integral of 8/(x^8)

\int \frac{8}{x ^{8}} d x

derivative bx^4

d er i v a t i v e b x^{4}

derivative of (1-x^4)

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