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受欢迎的微积分 >

integral of 8/(sqrt(e^x-2))

解答

\int \frac{8}{e ^{x} - 2} d x

解答

82 arctan (\frac{1}{2} (e^{x} - 2)) + C

求解步骤

\int \frac{8}{e ^{x} - 2} d x

提出常数:

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

= 8 \cdot \int \frac{1}{e ^{x} - 2} d x

使用换元积分法

= 8 \cdot \int \frac{2}{u ^{2} + 2} d u

提出常数:

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

= 8 \cdot 2 \cdot \int \frac{1}{u ^{2} + 2} d u

使用换元积分法

= 8 \cdot 2 \cdot \int \frac{1}{2 ( v ^{2} + 1 )} d v

提出常数:

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

= 8 \cdot 2 \cdot \frac{1}{2} \cdot \int \frac{1}{v ^{2} + 1} d v

使用积分常见定则:

\int \frac{1}{v ^{2} + 1} d v = arctan (v)

= 8 \cdot 2 \cdot \frac{1}{2} arctan (v)

代回

= 8 \cdot 2 \cdot \frac{1}{2} arctan (\frac{e ^{x} - 2}{2})

化简

8 \cdot 2 \cdot \frac{1}{2} arctan (\frac{e ^{x} - 2}{2}) : 82 arctan (\frac{1}{2} (e^{x} - 2))

= 82 arctan (\frac{1}{2} (e^{x} - 2))

解答补常数

= 82 arctan (\frac{1}{2} (e^{x} - 2)) + C

作图

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\int_{- \infty}^{15} r e^{\frac{r}{5}} d r

derivative of 3x^2+8

\frac{d}{d x} (3 x^{2} + 8)

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x \to \frac{1}{3} x lim (sin (x))

y^{^{'}} = e^{2 x - y}