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受欢迎的微积分 >

integral of (6x^2cos(2x^3+1))

解答

\int (6 x^{2} cos (2 x^{3} + 1)) d x

解答

sin (2 x^{3} + 1) + C

求解步骤

\int 6 x^{2} cos (2 x^{3} + 1) d x

提出常数:

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

= 6 \cdot \int x^{2} cos (2 x^{3} + 1) d x

使用换元积分法

= 6 \cdot \int \frac{cos ( 2 u + 1 )}{3} d u

提出常数:

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

= 6 \cdot \frac{1}{3} \cdot \int cos (2 u + 1) d u

使用换元积分法

= 6 \cdot \frac{1}{3} \cdot \int cos (v) \frac{1}{2} d v

提出常数:

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

= 6 \cdot \frac{1}{3} \cdot \frac{1}{2} \cdot \int cos (v) d v

使用积分常见定则:

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

= 6 \cdot \frac{1}{3} \cdot \frac{1}{2} sin (v)

代回

= 6 \cdot \frac{1}{3} \cdot \frac{1}{2} sin (2 x^{3} + 1)

化简

6 \cdot \frac{1}{3} \cdot \frac{1}{2} sin (2 x^{3} + 1) : sin (2 x^{3} + 1)

= sin (2 x^{3} + 1)

解答补常数

= sin (2 x^{3} + 1) + C

作图

流行的例子

derivative of 2sin^2(x+5sin(x)-3)

\frac{d}{d x} (2 sin^{2} (x) + 5 sin (x) - 3)

derivative of x/(e^{2x})

\frac{d}{d x} (\frac{x}{e ^{2 x}})

y^{^{'}} + 8 x^{2} y = x^{2}

derivative of (x+3^{2/3})

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

斜率 (0,0),(4,2)

s l o p e (0, 0), (4, 2)