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受欢迎的微积分 >

integral of 1/(e^xsin^2(e^{-x))}

解答

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

解答

cot (\frac{1}{e ^{x}}) + C

求解步骤

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

使用换元积分法

= \int \frac{1}{u ^{2} sin ^{2} ( \frac{1}{u} )} d u

使用换元积分法

= \int - csc^{2} (v) d v

提出常数:

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

= - \int csc^{2} (v) d v

使用积分常见定则:

\int csc^{2} (v) d v = - cot (v)

= - (- cot (v))

代回

= - (- cot (\frac{1}{e ^{x}}))

化简

= cot (\frac{1}{e ^{x}})

解答补常数

= cot (\frac{1}{e ^{x}}) + C

作图

流行的例子

integral of (x^9-3x^4)/(x^6)

\int \frac{x ^{9} - 3 x ^{4}}{x ^{6}} d x

integral of 1/(x^7)-2/(x^6)+9x+8

\int \frac{1}{x ^{7}} - \frac{2}{x ^{6}} + 9 x + 8 d x

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

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

integral of (3x+1)e^{-x}

\int (3 x + 1) e^{- x} d x

integral of (sin^2(ln(x)))/(xcos(ln(x)))

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