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受欢迎的微积分 >

integral of 7/(x^2+4)

解答

\int \frac{7}{x ^{2} + 4} d x

解答

\frac{7}{2} arctan (\frac{x}{2}) + C

求解步骤

\int \frac{7}{x ^{2} + 4} d x

提出常数:

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

= 7 \cdot \int \frac{1}{x ^{2} + 4} d x

使用换元积分法

= 7 \cdot \int \frac{1}{2 ( u ^{2} + 1 )} d u

提出常数:

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

= 7 \cdot \frac{1}{2} \cdot \int \frac{1}{u ^{2} + 1} d u

使用积分常见定则:

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

= 7 \cdot \frac{1}{2} arctan (u)

u = \frac{x}{2}

代回

= 7 \cdot \frac{1}{2} arctan (\frac{x}{2})

化简

7 \cdot \frac{1}{2} arctan (\frac{x}{2}) : \frac{7}{2} arctan (\frac{x}{2})

= \frac{7}{2} arctan (\frac{x}{2})

解答补常数

= \frac{7}{2} arctan (\frac{x}{2}) + C

作图

流行的例子

t^2y^'+y=sin(t)

t^{2} y^{^{'}} + y = sin (t)

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\frac{d}{d x} (- arcsin (\frac{a ^{2} - x ^{2}}{a}))

tangent y=x^2,\at x=-3/4

t an g e n t y = x^{2}, at x = - \frac{3}{4}

面积 y=x^2-2x,y=2-x

a re a y = x^{2} - 2 x, y = 2 - x

integral of 3^{4x+6}

\int 3^{4 x + 6} d x