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受欢迎的微积分 >

integral of 1/(8x^2-16x+64)

解答

\int \frac{1}{8 x ^{2} - 16 x + 64} d x

解答

\frac{1}{8 7} arctan (\frac{x - 1}{7}) + C

求解步骤

\int \frac{1}{8 x ^{2} - 16 x + 64} d x

对

8 x^{2} - 16 x + 64

配方:

8 (x - 1)^{2} + 56

= \int \frac{1}{8 ( x - 1 ) ^{2} + 56} d x

使用换元积分法

= \int \frac{1}{8 u ^{2} + 56} d u

使用换元积分法

= \int \frac{1}{8 7 ( v ^{2} + 1 )} d v

提出常数:

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

= \frac{1}{8 7} \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)

= \frac{1}{8 7} arctan (v)

代回

= \frac{1}{8 7} arctan (\frac{2 2}{2 14} (x - 1))

化简

\frac{1}{8 7} arctan (\frac{2 2}{2 14} (x - 1)) : \frac{1}{8 7} arctan (\frac{x - 1}{7})

= \frac{1}{8 7} arctan (\frac{x - 1}{7})

解答补常数

= \frac{1}{8 7} arctan (\frac{x - 1}{7}) + C

作图

流行的例子

(\partial)/(\partial t)(se^t)

\frac{\partial}{\partial t} (s e^{t})

f(x)=2^{3x^2-6}

f (x) = 2^{3 x^{2} - 6}

(dP)/(dt)=5sqrt(Pt),P(1)=3

\frac{d P}{d t} = 5 Pt, P (1) = 3

derivative of x/(4.5c(c-x))

\frac{d}{d x} (\frac{x}{4.5 c} (c - x))

limit as t approaches 6 of 8(t-5)(t-7)

t \to 6 lim (8 (t - 5) (t - 7))