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受欢迎的微积分 >

integral of (48x)/(4x^2+e)

解答

\int \frac{48 x}{4 x ^{2} + e} d x

解答

6 ln 4 x^{2} + e + C

求解步骤

\int \frac{48 x}{4 x ^{2} + e} d x

提出常数:

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

= 48 \cdot \int \frac{x}{4 x ^{2} + e} d x

使用换元积分法

= 48 \cdot \int \frac{1}{8 u} d u

提出常数:

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

= 48 \cdot \frac{1}{8} \cdot \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 48 \cdot \frac{1}{8} ln ∣ u ∣

u = 4 x^{2} + e

代回

= 48 \cdot \frac{1}{8} ln 4 x^{2} + e

化简

48 \cdot \frac{1}{8} ln 4 x^{2} + e : 6 ln 4 x^{2} + e

= 6 ln 4 x^{2} + e

解答补常数

= 6 ln 4 x^{2} + e + C

作图

流行的例子

integral from-1 to 1 of x/(x^2+1)

\int_{- 1}^{1} \frac{x}{x ^{2} + 1} d x

integral of 5x^{2/3}

\int 5 x^{\frac{2}{3}} d x

tangent y=6x^2-x^3,(1,5)

t an g e n t y = 6 x^{2} - x^{3}, (1, 5)

sum from n=0 to infinity of 1/(1!)

n = 0 \sum \infty \frac{1}{1 !}

integral of 5^{x+2}

\int 5^{x + 2} d x