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受欢迎的微积分 >

integral of 1/(sqrt(2x))cos(sqrt(2x))

解答

\int \frac{1}{2 x} cos (2 x) d x

解答

sin (2 x) + C

求解步骤

\int \frac{1}{2 x} cos (2 x) d x

使用换元积分法

= \int \frac{cos ( u )}{2 u} d u

提出常数:

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

= \frac{1}{2} \cdot \int \frac{cos ( u )}{u} d u

使用换元积分法

= \frac{1}{2} \cdot \int 2 cos (v) d v

提出常数:

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

= \frac{1}{2} \cdot 2 \cdot \int cos (v) d v

使用积分常见定则:

\int cos (v) d v = sin (v)

= \frac{1}{2} \cdot 2 sin (v)

代回

= \frac{1}{2} \cdot 2 sin (2 x)

化简

\frac{1}{2} \cdot 2 sin (2 x) : sin (2 x)

= sin (2 x)

解答补常数

= sin (2 x) + C

作图

流行的例子

limit as x approaches 8-of (x-9)/(x-8)

x \to 8 - lim (\frac{x - 9}{x - 8})

a re a 3 x, 7 x^{2}

derivative of 3^{x^4-2x^2}

\frac{d}{d x} (3^{x^{4} - 2 x^{2}})

limit as x approaches 0 of (5x-3)^2

x \to 0 lim ((5 x - 3)^{2})

inverselaplace ((2s+1))/((s+1)^2)

in v erse l a pl a ce \frac{( 2 s + 1 )}{( s + 1 ) ^{2}}